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ACM-ICPC Regional Asia Changchun 2013 Onsite
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A.cpp
/** Micro Mezz Macro Flation -- Overheated Economy ., Last Update: May. 7th 2014 **/ //{
/** Header .. **/ //{
#pragma comment(linker, "/STACK:36777216")
//#pragma GCC optimize ("O2")
#define LOCAL
//#include "testlib.h"
#include <functional>
#include <algorithm>
#include <iostream>
#include <fstream>
#include <sstream>
#include <iomanip>
#include <numeric>
#include <cstring>
#include <climits>
#include <cassert>
#include <complex>
#include <cstdio>
#include <string>
#include <vector>
#include <bitset>
#include <queue>
#include <stack>
#include <cmath>
#include <ctime>
#include <list>
#include <set>
#include <map>
//#include <tr1/unordered_set>
//#include <tr1/unordered_map>
//#include <array>
using namespace std;
#define REP(i, n) for (int i=0;i<n;++i)
#define FOR(i, a, b) for (int i=a;i<b;++i)
#define DWN(i, b, a) for (int i=b-1;i>=a;--i)
#define REP_1(i, n) for (int i=1;i<=n;++i)
#define FOR_1(i, a, b) for (int i=a;i<=b;++i)
#define DWN_1(i, b, a) for (int i=b;i>=a;--i)
#define REP_C(i, n) for (int n____=n,i=0;i<n____;++i)
#define FOR_C(i, a, b) for (int b____=b,i=a;i<b____;++i)
#define DWN_C(i, b, a) for (int a____=a,i=b-1;i>=a____;--i)
#define REP_N(i, n) for (i=0;i<n;++i)
#define FOR_N(i, a, b) for (i=a;i<b;++i)
#define DWN_N(i, b, a) for (i=b-1;i>=a;--i)
#define REP_1_C(i, n) for (int n____=n,i=1;i<=n____;++i)
#define FOR_1_C(i, a, b) for (int b____=b,i=a;i<=b____;++i)
#define DWN_1_C(i, b, a) for (int a____=a,i=b;i>=a____;--i)
#define REP_1_N(i, n) for (i=1;i<=n;++i)
#define FOR_1_N(i, a, b) for (i=a;i<=b;++i)
#define DWN_1_N(i, b, a) for (i=b;i>=a;--i)
#define REP_C_N(i, n) for (int n____=(i=0,n);i<n____;++i)
#define FOR_C_N(i, a, b) for (int b____=(i=0,b);i<b____;++i)
#define DWN_C_N(i, b, a) for (int a____=(i=b-1,a);i>=a____;--i)
#define REP_1_C_N(i, n) for (int n____=(i=1,n);i<=n____;++i)
#define FOR_1_C_N(i, a, b) for (int b____=(i=a,b);i<=b____;++i)
#define DWN_1_C_N(i, b, a) for (int a____=(i=b,a);i>=a____;--i)
#define ECH(it, A) for (__typeof(A.begin()) it=A.begin(); it != A.end(); ++it)
#define REP_S(i, str) for (char*i=str;*i;++i)
#define REP_L(i, hd, suc) for (int i=hd;i;i=suc[i])
#define REP_G(i, u) REP_L(i,hd[u],suc)
#define REP_SS(x, s) for (int x=s;x;x=(x-1)&s)
#define DO(n) for ( int ____n = n; ____n-->0; )
#define REP_2(i, j, n, m) REP(i, n) REP(j, m)
#define REP_2_1(i, j, n, m) REP_1(i, n) REP_1(j, m)
#define REP_3(i, j, k, n, m, l) REP(i, n) REP(j, m) REP(k, l)
#define REP_3_1(i, j, k, n, m, l) REP_1(i, n) REP_1(j, m) REP_1(k, l)
#define REP_4(i, j, k, ii, n, m, l, nn) REP(i, n) REP(j, m) REP(k, l) REP(ii, nn)
#define REP_4_1(i, j, k, ii, n, m, l, nn) REP_1(i, n) REP_1(j, m) REP_1(k, l) REP_1(ii, nn)
#define ALL(A) A.begin(), A.end()
#define LLA(A) A.rbegin(), A.rend()
#define CPY(A, B) memcpy(A, B, sizeof(A))
#define INS(A, P, B) A.insert(A.begin() + P, B)
#define ERS(A, P) A.erase(A.begin() + P)
#define LBD(A, x) (lower_bound(ALL(A), x) - A.begin())
#define UBD(A, x) (lower_bound(ALL(A), x) - A.begin())
#define CTN(T, x) (T.find(x) != T.end())
#define SZ(A) int((A).size())
#define PB push_back
#define MP(A, B) make_pair(A, B)
#define PTT pair<T, T>
#define Ts *this
#define rTs return Ts
#define fi first
#define se second
#define re real()
#define im imag()
#define Rush for(int ____T=RD(); ____T--;)
#define Display(A, n, m) { \
REP(i, n){ \
REP(j, m-1) cout << A[i][j] << " "; \
cout << A[i][m-1] << endl; \
} \
}
#define Display_1(A, n, m) { \
REP_1(i, n){ \
REP_1(j, m-1) cout << A[i][j] << " "; \
cout << A[i][m] << endl; \
} \
}
typedef long long LL;
//typedef long double DB;
typedef double DB;
typedef unsigned uint;
typedef unsigned long long uLL;
typedef vector<int> VI;
typedef vector<char> VC;
typedef vector<string> VS;
typedef vector<LL> VL;
typedef vector<DB> VF;
typedef set<int> SI;
typedef set<string> SS;
typedef map<int, int> MII;
typedef map<string, int> MSI;
typedef pair<int, int> PII;
typedef pair<LL, LL> PLL;
typedef vector<PII> VII;
typedef vector<VI> VVI;
typedef vector<VII> VVII;
template<class T> inline T& RD(T &);
template<class T> inline void OT(const T &);
//inline int RD(){int x; return RD(x);}
inline LL RD(){LL x; return RD(x);}
inline DB& RF(DB &);
inline DB RF(){DB x; return RF(x);}
inline char* RS(char *s);
inline char& RC(char &c);
inline char RC();
inline char& RC(char &c){scanf(" %c", &c); return c;}
inline char RC(){char c; return RC(c);}
//inline char& RC(char &c){c = getchar(); return c;}
//inline char RC(){return getchar();}
template<class T> inline T& RDD(T &);
inline LL RDD(){LL x; return RDD(x);}
template<class T0, class T1> inline T0& RD(T0 &x0, T1 &x1){RD(x0), RD(x1); return x0;}
template<class T0, class T1, class T2> inline T0& RD(T0 &x0, T1 &x1, T2 &x2){RD(x0), RD(x1), RD(x2); return x0;}
template<class T0, class T1, class T2, class T3> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3){RD(x0), RD(x1), RD(x2), RD(x3); return x0;}
template<class T0, class T1, class T2, class T3, class T4> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4); return x0;}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5); return x0;}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5, T6 &x6){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5), RD(x6); return x0;}
template<class T0, class T1> inline void OT(const T0 &x0, const T1 &x1){OT(x0), OT(x1);}
template<class T0, class T1, class T2> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2){OT(x0), OT(x1), OT(x2);}
template<class T0, class T1, class T2, class T3> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3){OT(x0), OT(x1), OT(x2), OT(x3);}
template<class T0, class T1, class T2, class T3, class T4> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3, const T4 &x4){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3, const T4 &x4, const T5 &x5){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3, const T4 &x4, const T5 &x5, const T6 &x6){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5), OT(x6);}
inline char& RC(char &a, char &b){RC(a), RC(b); return a;}
inline char& RC(char &a, char &b, char &c){RC(a), RC(b), RC(c); return a;}
inline char& RC(char &a, char &b, char &c, char &d){RC(a), RC(b), RC(c), RC(d); return a;}
inline char& RC(char &a, char &b, char &c, char &d, char &e){RC(a), RC(b), RC(c), RC(d), RC(e); return a;}
inline char& RC(char &a, char &b, char &c, char &d, char &e, char &f){RC(a), RC(b), RC(c), RC(d), RC(e), RC(f); return a;}
inline char& RC(char &a, char &b, char &c, char &d, char &e, char &f, char &g){RC(a), RC(b), RC(c), RC(d), RC(e), RC(f), RC(g); return a;}
inline DB& RF(DB &a, DB &b){RF(a), RF(b); return a;}
inline DB& RF(DB &a, DB &b, DB &c){RF(a), RF(b), RF(c); return a;}
inline DB& RF(DB &a, DB &b, DB &c, DB &d){RF(a), RF(b), RF(c), RF(d); return a;}
inline DB& RF(DB &a, DB &b, DB &c, DB &d, DB &e){RF(a), RF(b), RF(c), RF(d), RF(e); return a;}
inline DB& RF(DB &a, DB &b, DB &c, DB &d, DB &e, DB &f){RF(a), RF(b), RF(c), RF(d), RF(e), RF(f); return a;}
inline DB& RF(DB &a, DB &b, DB &c, DB &d, DB &e, DB &f, DB &g){RF(a), RF(b), RF(c), RF(d), RF(e), RF(f), RF(g); return a;}
inline void RS(char *s1, char *s2){RS(s1), RS(s2);}
inline void RS(char *s1, char *s2, char *s3){RS(s1), RS(s2), RS(s3);}
template<class T0,class T1>inline void RDD(T0&a, T1&b){RDD(a),RDD(b);}
template<class T0,class T1,class T2>inline void RDD(T0&a, T1&b, T2&c){RDD(a),RDD(b),RDD(c);}
template<class T> inline void RST(T &A){memset(A, 0, sizeof(A));}
template<class T> inline void FLC(T &A, int x){memset(A, x, sizeof(A));}
template<class T> inline void CLR(T &A){A.clear();}
template<class T0, class T1> inline void RST(T0 &A0, T1 &A1){RST(A0), RST(A1);}
template<class T0, class T1, class T2> inline void RST(T0 &A0, T1 &A1, T2 &A2){RST(A0), RST(A1), RST(A2);}
template<class T0, class T1, class T2, class T3> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3){RST(A0), RST(A1), RST(A2), RST(A3);}
template<class T0, class T1, class T2, class T3, class T4> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5), RST(A6);}
template<class T0, class T1> inline void FLC(T0 &A0, T1 &A1, int x){FLC(A0, x), FLC(A1, x);}
template<class T0, class T1, class T2> inline void FLC(T0 &A0, T1 &A1, T2 &A2, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x);}
template<class T0, class T1, class T2, class T3> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x);}
template<class T0, class T1, class T2, class T3, class T4> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x), FLC(A5, x);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x), FLC(A5, x), FLC(A6, x);}
template<class T> inline void CLR(priority_queue<T, vector<T>, less<T> > &Q){while (!Q.empty()) Q.pop();}
template<class T> inline void CLR(priority_queue<T, vector<T>, greater<T> > &Q){while (!Q.empty()) Q.pop();}
template<class T> inline void CLR(stack<T> &S){while (!S.empty()) S.pop();}
template<class T0, class T1> inline void CLR(T0 &A0, T1 &A1){CLR(A0), CLR(A1);}
template<class T0, class T1, class T2> inline void CLR(T0 &A0, T1 &A1, T2 &A2){CLR(A0), CLR(A1), CLR(A2);}
template<class T0, class T1, class T2, class T3> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3){CLR(A0), CLR(A1), CLR(A2), CLR(A3);}
template<class T0, class T1, class T2, class T3, class T4> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5), CLR(A6);}
template<class T> inline void CLR(T &A, int n){REP(i, n) CLR(A[i]);}
template<class T> inline bool EPT(T &a){return a.empty();}
template<class T> inline T& SRT(T &A){sort(ALL(A)); return A;}
template<class T, class C> inline T& SRT(T &A, C B){sort(ALL(A), B); return A;}
template<class T> inline T& RVS(T &A){reverse(ALL(A)); return A;}
template<class T> inline T& UNQQ(T &A){A.resize(unique(ALL(A))-A.begin());return A;}
template<class T> inline T& UNQ(T &A){SRT(A);return UNQQ(A);}
//}
/** Constant List .. **/ //{
const int MOD = int(1e9) + 7;
const int INF = 0x3f3f3f3f;
const LL INFF = 0x3f3f3f3f3f3f3f3fLL;
const DB EPS = 1e-9;
const DB OO = 1e20;
const DB PI = acos(-1.0); //M_PI;
const int dx[] = {-1, 0, 1, 0};
const int dy[] = {0, 1, 0, -1};
//}
/** Add On .. **/ //{
// <<= '0. Nichi Joo ., //{
template<class T> inline T& checkMin(T &a,const T b){if (b<a) a=b;return a;}
template<class T> inline T& checkMax(T &a,const T b){if (a<b) a=b;return a;}
template<class T> inline T& checkMin(T &a, T &b, const T x){checkMin(a, x), checkMin(b, x);return a;}
template<class T> inline T& checkMax(T &a, T &b, const T x){checkMax(a, x), checkMax(b, x);return a;}
template <class T, class C> inline T& checkMin(T& a, const T b, C c){if (c(b,a)) a = b;return a;}
template <class T, class C> inline T& checkMax(T& a, const T b, C c){if (c(a,b)) a = b;return a;}
template<class T> inline T min(T a, T b, T c){return min(min(a, b), c);}
template<class T> inline T max(T a, T b, T c){return max(max(a, b), c);}
template<class T> inline T min(T a, T b, T c, T d){return min(min(a, b), min(c, d));}
template<class T> inline T max(T a, T b, T c, T d){return max(max(a, b), max(c, d));}
template<class T> inline T min(T a, T b, T c, T d, T e){return min(min(min(a,b),min(c,d)),e);}
template<class T> inline T max(T a, T b, T c, T d, T e){return max(max(max(a,b),max(c,d)),e);}
template<class T> inline T sqr(T a){return a*a;}
template<class T> inline T cub(T a){return a*a*a;}
template<class T> inline T ceil(T x, T y){return (x - 1) / y + 1;}
template<class T> T abs(T x){return x>0?x:-x;}
inline int sgn(DB x){return x < -EPS ? -1 : x > EPS;}
inline int sgn(DB x, DB y){return sgn(x - y);}
inline DB cos(DB a, DB b, DB c){return (sqr(a)+sqr(b)-sqr(c))/(2*a*b);}
inline DB cot(DB x){return 1./tan(x);};
inline DB sec(DB x){return 1./cos(x);};
inline DB csc(DB x){return 1./sin(x);};
//}
// <<= '1. Bitwise Operation ., //{
namespace BO{
inline bool _1(int x, int i){return bool(x&1<<i);}
inline bool _1(LL x, int i){return bool(x&1LL<<i);}
inline LL _1(int i){return 1LL<<i;}
inline LL _U(int i){return _1(i) - 1;};
inline int reverse_bits(int x){
x = ((x >> 1) & 0x55555555) | ((x << 1) & 0xaaaaaaaa);
x = ((x >> 2) & 0x33333333) | ((x << 2) & 0xcccccccc);
x = ((x >> 4) & 0x0f0f0f0f) | ((x << 4) & 0xf0f0f0f0);
x = ((x >> 8) & 0x00ff00ff) | ((x << 8) & 0xff00ff00);
x = ((x >>16) & 0x0000ffff) | ((x <<16) & 0xffff0000);
return x;
}
inline LL reverse_bits(LL x){
x = ((x >> 1) & 0x5555555555555555LL) | ((x << 1) & 0xaaaaaaaaaaaaaaaaLL);
x = ((x >> 2) & 0x3333333333333333LL) | ((x << 2) & 0xccccccccccccccccLL);
x = ((x >> 4) & 0x0f0f0f0f0f0f0f0fLL) | ((x << 4) & 0xf0f0f0f0f0f0f0f0LL);
x = ((x >> 8) & 0x00ff00ff00ff00ffLL) | ((x << 8) & 0xff00ff00ff00ff00LL);
x = ((x >>16) & 0x0000ffff0000ffffLL) | ((x <<16) & 0xffff0000ffff0000LL);
x = ((x >>32) & 0x00000000ffffffffLL) | ((x <<32) & 0xffffffff00000000LL);
return x;
}
template<class T> inline bool odd(T x){return x&1;}
template<class T> inline bool even(T x){return !odd(x);}
template<class T> inline T low_bit(T x) {return x & -x;}
template<class T> inline T high_bit(T x) {T p = low_bit(x);while (p != x) x -= p, p = low_bit(x);return p;}
template<class T> inline T cover_bit(T x){T p = 1; while (p < x) p <<= 1;return p;}
template<class T> inline int cover_idx(T x){int p = 0; while (_1(p) < x ) ++p; return p;}
inline int clz(int x){return __builtin_clz(x);}
inline int clz(LL x){return __builtin_clzll(x);}
inline int ctz(int x){return __builtin_ctz(x);}
inline int ctz(LL x){return __builtin_ctzll(x);}
inline int lg2(int x){return !x ? -1 : 31 - clz(x);}
inline int lg2(LL x){return !x ? -1 : 63 - clz(x);}
inline int low_idx(int x){return !x ? -1 : ctz(x);}
inline int low_idx(LL x){return !x ? -1 : ctz(x);}
inline int high_idx(int x){return lg2(x);}
inline int high_idx(LL x){return lg2(x);}
inline int parity(int x){return __builtin_parity(x);}
inline int parity(LL x){return __builtin_parityll(x);}
inline int count_bits(int x){return __builtin_popcount(x);}
inline int count_bits(LL x){return __builtin_popcountll(x);}
} using namespace BO;//}
//}
/** I/O Accelerator Interface .. **/ //{
#define g (c=getchar())
#define d isdigit(g)
#define p x=x*10+c-'0'
#define n x=x*10+'0'-c
#define pp l/=10,p
#define nn l/=10,n
template<class T> inline T& RD(T &x){
char c;while(!d);x=c-'0';while(d)p;
return x;
}
template<class T> inline T& RDD(T &x){
char c;while(g,c!='-'&&!isdigit(c));
if (c=='-'){x='0'-g;while(d)n;}
else{x=c-'0';while(d)p;}
return x;
}
inline DB& RF(DB &x){
//scanf("%lf", &x);
char c;while(g,c!='-'&&c!='.'&&!isdigit(c));
if(c=='-')if(g=='.'){x=0;DB l=1;while(d)nn;x*=l;}
else{x='0'-c;while(d)n;if(c=='.'){DB l=1;while(d)nn;x*=l;}}
else if(c=='.'){x=0;DB l=1;while(d)pp;x*=l;}
else{x=c-'0';while(d)p;if(c=='.'){DB l=1;while(d)pp;x*=l;}}
return x;
}
#undef nn
#undef pp
#undef n
#undef p
#undef d
#undef g
inline char* RS(char *s){
//gets(s);
scanf("%s", s);
return s;
}
LL last_ans; int Case; template<class T> inline void OT(const T &x){
//printf("Case #%d: ", ++Case);
//printf("%lld\n", x);
//printf("%.9f\n", x);
printf("%d\n", x);
//cout << x << endl;
//last_ans = x;
}
//}
//}/* .................................................................................................................................. */
const int N = int(1e6) + 9;
char str[N];
int main(){
Rush{
int n, m; RD(n, m); RS(str);
REP(i, n){
REP(j, m) printf("%c", str[i*m+j]);
puts("");
}
}
}
Raw
B.cpp
/** Micro Mezz Macro Flation -- Overheated Economy ., Last Update: May. 7th 2014 **/ //{
/** Header .. **/ //{
#pragma comment(linker, "/STACK:36777216")
//#pragma GCC optimize ("O2")
#define LOCAL
//#include "testlib.h"
#include <functional>
#include <algorithm>
#include <iostream>
#include <fstream>
#include <sstream>
#include <iomanip>
#include <numeric>
#include <cstring>
#include <climits>
#include <cassert>
#include <complex>
#include <cstdio>
#include <string>
#include <vector>
#include <bitset>
#include <queue>
#include <stack>
#include <cmath>
#include <ctime>
#include <list>
#include <set>
#include <map>
//#include <tr1/unordered_set>
//#include <tr1/unordered_map>
//#include <array>
using namespace std;
#define REP(i, n) for (int i=0;i<n;++i)
#define FOR(i, a, b) for (int i=a;i<b;++i)
#define DWN(i, b, a) for (int i=b-1;i>=a;--i)
#define REP_1(i, n) for (int i=1;i<=n;++i)
#define FOR_1(i, a, b) for (int i=a;i<=b;++i)
#define DWN_1(i, b, a) for (int i=b;i>=a;--i)
#define REP_C(i, n) for (int n____=n,i=0;i<n____;++i)
#define FOR_C(i, a, b) for (int b____=b,i=a;i<b____;++i)
#define DWN_C(i, b, a) for (int a____=a,i=b-1;i>=a____;--i)
#define REP_N(i, n) for (i=0;i<n;++i)
#define FOR_N(i, a, b) for (i=a;i<b;++i)
#define DWN_N(i, b, a) for (i=b-1;i>=a;--i)
#define REP_1_C(i, n) for (int n____=n,i=1;i<=n____;++i)
#define FOR_1_C(i, a, b) for (int b____=b,i=a;i<=b____;++i)
#define DWN_1_C(i, b, a) for (int a____=a,i=b;i>=a____;--i)
#define REP_1_N(i, n) for (i=1;i<=n;++i)
#define FOR_1_N(i, a, b) for (i=a;i<=b;++i)
#define DWN_1_N(i, b, a) for (i=b;i>=a;--i)
#define REP_C_N(i, n) for (int n____=(i=0,n);i<n____;++i)
#define FOR_C_N(i, a, b) for (int b____=(i=0,b);i<b____;++i)
#define DWN_C_N(i, b, a) for (int a____=(i=b-1,a);i>=a____;--i)
#define REP_1_C_N(i, n) for (int n____=(i=1,n);i<=n____;++i)
#define FOR_1_C_N(i, a, b) for (int b____=(i=a,b);i<=b____;++i)
#define DWN_1_C_N(i, b, a) for (int a____=(i=b,a);i>=a____;--i)
#define ECH(it, A) for (__typeof(A.begin()) it=A.begin(); it != A.end(); ++it)
#define REP_S(i, str) for (char*i=str;*i;++i)
#define REP_L(i, hd, suc) for (int i=hd;i;i=suc[i])
#define REP_G(i, u) REP_L(i,hd[u],suc)
#define REP_SS(x, s) for (int x=s;x;x=(x-1)&s)
#define DO(n) for ( int ____n = n; ____n-->0; )
#define REP_2(i, j, n, m) REP(i, n) REP(j, m)
#define REP_2_1(i, j, n, m) REP_1(i, n) REP_1(j, m)
#define REP_3(i, j, k, n, m, l) REP(i, n) REP(j, m) REP(k, l)
#define REP_3_1(i, j, k, n, m, l) REP_1(i, n) REP_1(j, m) REP_1(k, l)
#define REP_4(i, j, k, ii, n, m, l, nn) REP(i, n) REP(j, m) REP(k, l) REP(ii, nn)
#define REP_4_1(i, j, k, ii, n, m, l, nn) REP_1(i, n) REP_1(j, m) REP_1(k, l) REP_1(ii, nn)
#define ALL(A) A.begin(), A.end()
#define LLA(A) A.rbegin(), A.rend()
#define CPY(A, B) memcpy(A, B, sizeof(A))
#define INS(A, P, B) A.insert(A.begin() + P, B)
#define ERS(A, P) A.erase(A.begin() + P)
#define LBD(A, x) (lower_bound(ALL(A), x) - A.begin())
#define UBD(A, x) (lower_bound(ALL(A), x) - A.begin())
#define CTN(T, x) (T.find(x) != T.end())
#define SZ(A) int((A).size())
#define PB push_back
#define MP(A, B) make_pair(A, B)
#define PTT pair<T, T>
#define Ts *this
#define rTs return Ts
#define fi first
#define se second
#define re real()
#define im imag()
#define Rush for(int ____T=RD(); ____T--;)
#define Display(A, n, m) { \
REP(i, n){ \
REP(j, m-1) cout << A[i][j] << " "; \
cout << A[i][m-1] << endl; \
} \
}
#define Display_1(A, n, m) { \
REP_1(i, n){ \
REP_1(j, m-1) cout << A[i][j] << " "; \
cout << A[i][m] << endl; \
} \
}
typedef long long LL;
//typedef long double DB;
typedef double DB;
typedef unsigned uint;
typedef unsigned long long uLL;
typedef vector<int> VI;
typedef vector<char> VC;
typedef vector<string> VS;
typedef vector<LL> VL;
typedef vector<DB> VF;
typedef set<int> SI;
typedef set<string> SS;
typedef map<int, int> MII;
typedef map<string, int> MSI;
typedef pair<int, int> PII;
typedef pair<LL, LL> PLL;
typedef vector<PII> VII;
typedef vector<VI> VVI;
typedef vector<VII> VVII;
template<class T> inline T& RD(T &);
template<class T> inline void OT(const T &);
//inline int RD(){int x; return RD(x);}
inline LL RD(){LL x; return RD(x);}
inline DB& RF(DB &);
inline DB RF(){DB x; return RF(x);}
inline char* RS(char *s);
inline char& RC(char &c);
inline char RC();
inline char& RC(char &c){scanf(" %c", &c); return c;}
inline char RC(){char c; return RC(c);}
//inline char& RC(char &c){c = getchar(); return c;}
//inline char RC(){return getchar();}
template<class T> inline T& RDD(T &);
inline LL RDD(){LL x; return RDD(x);}
template<class T0, class T1> inline T0& RD(T0 &x0, T1 &x1){RD(x0), RD(x1); return x0;}
template<class T0, class T1, class T2> inline T0& RD(T0 &x0, T1 &x1, T2 &x2){RD(x0), RD(x1), RD(x2); return x0;}
template<class T0, class T1, class T2, class T3> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3){RD(x0), RD(x1), RD(x2), RD(x3); return x0;}
template<class T0, class T1, class T2, class T3, class T4> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4); return x0;}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5); return x0;}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5, T6 &x6){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5), RD(x6); return x0;}
template<class T0, class T1> inline void OT(const T0 &x0, const T1 &x1){OT(x0), OT(x1);}
template<class T0, class T1, class T2> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2){OT(x0), OT(x1), OT(x2);}
template<class T0, class T1, class T2, class T3> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3){OT(x0), OT(x1), OT(x2), OT(x3);}
template<class T0, class T1, class T2, class T3, class T4> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3, const T4 &x4){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3, const T4 &x4, const T5 &x5){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3, const T4 &x4, const T5 &x5, const T6 &x6){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5), OT(x6);}
inline char& RC(char &a, char &b){RC(a), RC(b); return a;}
inline char& RC(char &a, char &b, char &c){RC(a), RC(b), RC(c); return a;}
inline char& RC(char &a, char &b, char &c, char &d){RC(a), RC(b), RC(c), RC(d); return a;}
inline char& RC(char &a, char &b, char &c, char &d, char &e){RC(a), RC(b), RC(c), RC(d), RC(e); return a;}
inline char& RC(char &a, char &b, char &c, char &d, char &e, char &f){RC(a), RC(b), RC(c), RC(d), RC(e), RC(f); return a;}
inline char& RC(char &a, char &b, char &c, char &d, char &e, char &f, char &g){RC(a), RC(b), RC(c), RC(d), RC(e), RC(f), RC(g); return a;}
inline DB& RF(DB &a, DB &b){RF(a), RF(b); return a;}
inline DB& RF(DB &a, DB &b, DB &c){RF(a), RF(b), RF(c); return a;}
inline DB& RF(DB &a, DB &b, DB &c, DB &d){RF(a), RF(b), RF(c), RF(d); return a;}
inline DB& RF(DB &a, DB &b, DB &c, DB &d, DB &e){RF(a), RF(b), RF(c), RF(d), RF(e); return a;}
inline DB& RF(DB &a, DB &b, DB &c, DB &d, DB &e, DB &f){RF(a), RF(b), RF(c), RF(d), RF(e), RF(f); return a;}
inline DB& RF(DB &a, DB &b, DB &c, DB &d, DB &e, DB &f, DB &g){RF(a), RF(b), RF(c), RF(d), RF(e), RF(f), RF(g); return a;}
inline void RS(char *s1, char *s2){RS(s1), RS(s2);}
inline void RS(char *s1, char *s2, char *s3){RS(s1), RS(s2), RS(s3);}
template<class T0,class T1>inline void RDD(T0&a, T1&b){RDD(a),RDD(b);}
template<class T0,class T1,class T2>inline void RDD(T0&a, T1&b, T2&c){RDD(a),RDD(b),RDD(c);}
template<class T> inline void RST(T &A){memset(A, 0, sizeof(A));}
template<class T> inline void FLC(T &A, int x){memset(A, x, sizeof(A));}
template<class T> inline void CLR(T &A){A.clear();}
template<class T0, class T1> inline void RST(T0 &A0, T1 &A1){RST(A0), RST(A1);}
template<class T0, class T1, class T2> inline void RST(T0 &A0, T1 &A1, T2 &A2){RST(A0), RST(A1), RST(A2);}
template<class T0, class T1, class T2, class T3> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3){RST(A0), RST(A1), RST(A2), RST(A3);}
template<class T0, class T1, class T2, class T3, class T4> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5), RST(A6);}
template<class T0, class T1> inline void FLC(T0 &A0, T1 &A1, int x){FLC(A0, x), FLC(A1, x);}
template<class T0, class T1, class T2> inline void FLC(T0 &A0, T1 &A1, T2 &A2, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x);}
template<class T0, class T1, class T2, class T3> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x);}
template<class T0, class T1, class T2, class T3, class T4> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x), FLC(A5, x);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x), FLC(A5, x), FLC(A6, x);}
template<class T> inline void CLR(priority_queue<T, vector<T>, less<T> > &Q){while (!Q.empty()) Q.pop();}
template<class T> inline void CLR(priority_queue<T, vector<T>, greater<T> > &Q){while (!Q.empty()) Q.pop();}
template<class T> inline void CLR(stack<T> &S){while (!S.empty()) S.pop();}
template<class T0, class T1> inline void CLR(T0 &A0, T1 &A1){CLR(A0), CLR(A1);}
template<class T0, class T1, class T2> inline void CLR(T0 &A0, T1 &A1, T2 &A2){CLR(A0), CLR(A1), CLR(A2);}
template<class T0, class T1, class T2, class T3> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3){CLR(A0), CLR(A1), CLR(A2), CLR(A3);}
template<class T0, class T1, class T2, class T3, class T4> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5), CLR(A6);}
template<class T> inline void CLR(T &A, int n){REP(i, n) CLR(A[i]);}
template<class T> inline bool EPT(T &a){return a.empty();}
template<class T> inline T& SRT(T &A){sort(ALL(A)); return A;}
template<class T, class C> inline T& SRT(T &A, C B){sort(ALL(A), B); return A;}
template<class T> inline T& RVS(T &A){reverse(ALL(A)); return A;}
template<class T> inline T& UNQQ(T &A){A.resize(unique(ALL(A))-A.begin());return A;}
template<class T> inline T& UNQ(T &A){SRT(A);return UNQQ(A);}
//}
/** Constant List .. **/ //{
const int MOD = int(1e9) + 7;
const int INF = 0x3f3f3f3f;
const LL INFF = 0x3f3f3f3f3f3f3f3fLL;
const DB EPS = 1e-9;
const DB OO = 1e20;
const DB PI = acos(-1.0); //M_PI;
const int dx[] = {-1, 0, 1, 0};
const int dy[] = {0, 1, 0, -1};
//}
/** Add On .. **/ //{
// <<= '0. Nichi Joo ., //{
template<class T> inline T& checkMin(T &a,const T b){if (b<a) a=b;return a;}
template<class T> inline T& checkMax(T &a,const T b){if (a<b) a=b;return a;}
template<class T> inline T& checkMin(T &a, T &b, const T x){checkMin(a, x), checkMin(b, x);return a;}
template<class T> inline T& checkMax(T &a, T &b, const T x){checkMax(a, x), checkMax(b, x);return a;}
template <class T, class C> inline T& checkMin(T& a, const T b, C c){if (c(b,a)) a = b;return a;}
template <class T, class C> inline T& checkMax(T& a, const T b, C c){if (c(a,b)) a = b;return a;}
template<class T> inline T min(T a, T b, T c){return min(min(a, b), c);}
template<class T> inline T max(T a, T b, T c){return max(max(a, b), c);}
template<class T> inline T min(T a, T b, T c, T d){return min(min(a, b), min(c, d));}
template<class T> inline T max(T a, T b, T c, T d){return max(max(a, b), max(c, d));}
template<class T> inline T min(T a, T b, T c, T d, T e){return min(min(min(a,b),min(c,d)),e);}
template<class T> inline T max(T a, T b, T c, T d, T e){return max(max(max(a,b),max(c,d)),e);}
template<class T> inline T sqr(T a){return a*a;}
template<class T> inline T cub(T a){return a*a*a;}
template<class T> inline T ceil(T x, T y){return (x - 1) / y + 1;}
template<class T> T abs(T x){return x>0?x:-x;}
inline int sgn(DB x){return x < -EPS ? -1 : x > EPS;}
inline int sgn(DB x, DB y){return sgn(x - y);}
inline DB cos(DB a, DB b, DB c){return (sqr(a)+sqr(b)-sqr(c))/(2*a*b);}
inline DB cot(DB x){return 1./tan(x);};
inline DB sec(DB x){return 1./cos(x);};
inline DB csc(DB x){return 1./sin(x);};
//}
// <<= '1. Bitwise Operation ., //{
namespace BO{
inline bool _1(int x, int i){return bool(x&1<<i);}
inline bool _1(LL x, int i){return bool(x&1LL<<i);}
inline LL _1(int i){return 1LL<<i;}
inline LL _U(int i){return _1(i) - 1;};
inline int reverse_bits(int x){
x = ((x >> 1) & 0x55555555) | ((x << 1) & 0xaaaaaaaa);
x = ((x >> 2) & 0x33333333) | ((x << 2) & 0xcccccccc);
x = ((x >> 4) & 0x0f0f0f0f) | ((x << 4) & 0xf0f0f0f0);
x = ((x >> 8) & 0x00ff00ff) | ((x << 8) & 0xff00ff00);
x = ((x >>16) & 0x0000ffff) | ((x <<16) & 0xffff0000);
return x;
}
inline LL reverse_bits(LL x){
x = ((x >> 1) & 0x5555555555555555LL) | ((x << 1) & 0xaaaaaaaaaaaaaaaaLL);
x = ((x >> 2) & 0x3333333333333333LL) | ((x << 2) & 0xccccccccccccccccLL);
x = ((x >> 4) & 0x0f0f0f0f0f0f0f0fLL) | ((x << 4) & 0xf0f0f0f0f0f0f0f0LL);
x = ((x >> 8) & 0x00ff00ff00ff00ffLL) | ((x << 8) & 0xff00ff00ff00ff00LL);
x = ((x >>16) & 0x0000ffff0000ffffLL) | ((x <<16) & 0xffff0000ffff0000LL);
x = ((x >>32) & 0x00000000ffffffffLL) | ((x <<32) & 0xffffffff00000000LL);
return x;
}
template<class T> inline bool odd(T x){return x&1;}
template<class T> inline bool even(T x){return !odd(x);}
template<class T> inline T low_bit(T x) {return x & -x;}
template<class T> inline T high_bit(T x) {T p = low_bit(x);while (p != x) x -= p, p = low_bit(x);return p;}
template<class T> inline T cover_bit(T x){T p = 1; while (p < x) p <<= 1;return p;}
template<class T> inline int cover_idx(T x){int p = 0; while (_1(p) < x ) ++p; return p;}
inline int clz(int x){return __builtin_clz(x);}
inline int clz(LL x){return __builtin_clzll(x);}
inline int ctz(int x){return __builtin_ctz(x);}
inline int ctz(LL x){return __builtin_ctzll(x);}
inline int lg2(int x){return !x ? -1 : 31 - clz(x);}
inline int lg2(LL x){return !x ? -1 : 63 - clz(x);}
inline int low_idx(int x){return !x ? -1 : ctz(x);}
inline int low_idx(LL x){return !x ? -1 : ctz(x);}
inline int high_idx(int x){return lg2(x);}
inline int high_idx(LL x){return lg2(x);}
inline int parity(int x){return __builtin_parity(x);}
inline int parity(LL x){return __builtin_parityll(x);}
inline int count_bits(int x){return __builtin_popcount(x);}
inline int count_bits(LL x){return __builtin_popcountll(x);}
} using namespace BO;//}
//}
/** I/O Accelerator Interface .. **/ //{
#define g (c=getchar())
#define d isdigit(g)
#define p x=x*10+c-'0'
#define n x=x*10+'0'-c
#define pp l/=10,p
#define nn l/=10,n
template<class T> inline T& RD(T &x){
char c;while(!d);x=c-'0';while(d)p;
return x;
}
template<class T> inline T& RDD(T &x){
char c;while(g,c!='-'&&!isdigit(c));
if (c=='-'){x='0'-g;while(d)n;}
else{x=c-'0';while(d)p;}
return x;
}
inline DB& RF(DB &x){
//scanf("%lf", &x);
char c;while(g,c!='-'&&c!='.'&&!isdigit(c));
if(c=='-')if(g=='.'){x=0;DB l=1;while(d)nn;x*=l;}
else{x='0'-c;while(d)n;if(c=='.'){DB l=1;while(d)nn;x*=l;}}
else if(c=='.'){x=0;DB l=1;while(d)pp;x*=l;}
else{x=c-'0';while(d)p;if(c=='.'){DB l=1;while(d)pp;x*=l;}}
return x;
}
#undef nn
#undef pp
#undef n
#undef p
#undef d
#undef g
inline char* RS(char *s){
//gets(s);
scanf("%s", s);
return s;
}
LL last_ans; int Case; template<class T> inline void OT(const T &x){
//printf("Case #%d: ", ++Case);
//printf("%lld\n", x);
//printf("%.9f\n", x);
printf("%d\n", x);
//cout << x << endl;
//last_ans = x;
}
//}
//}/* .................................................................................................................................. */
const int N = int(1e3) + 9;
struct base_phi_number{
int A[2*N], *a;
int lo, hi;
void out(){
DWN_1(i, hi, 0) printf("%d", a[i]); if (lo < 0) putchar('.');
DWN(i, 0, lo) printf("%d", a[i]);
puts("");
}
void init(int n){
RST(A); a=A+N; lo = 0, hi = 0, a[0] = n;
bool upd; do{
upd = 0; DWN_1(i, hi, lo) if (a[i] >= 2){
a[i+1] += a[i]/2;
a[i-2] += a[i]/2;
a[i] %= 2, upd = 1;
}
DWN_1(i, hi, lo) if (a[i] && a[i-1]){
int d = min(a[i], a[i-1]);
a[i+1] += d, a[i] -= d, a[i-1] -= d;
upd = 1;
}
while (a[hi+1]) ++hi;
while (a[lo-1] || a[lo-2]) --lo;
while (!a[lo]) ++lo;
} while(upd);
}
} A;
int main(){
#ifndef ONLINE_JUDGE
freopen("in.txt", "r", stdin);
//freopen("out.txt", "w", stdout);
#endif
int n; while (~scanf("%d", &n)){
A.init(n);
A.out();
}
}
/*
11
100
200
1001
*/
/*
101010101
1001
1001
1001
1001
1011111101
*/
Raw
C.cpp
/** Micro Mezz Macro Flation -- Overheated Economy ., Last Update: May. 7th 2014 **/ //{
/** Header .. **/ //{
#pragma comment(linker, "/STACK:36777216")
//#pragma GCC optimize ("O2")
#define LOCAL
//#include "testlib.h"
#include <functional>
#include <algorithm>
#include <iostream>
#include <fstream>
#include <sstream>
#include <iomanip>
#include <numeric>
#include <cstring>
#include <climits>
#include <cassert>
#include <complex>
#include <cstdio>
#include <string>
#include <vector>
#include <bitset>
#include <queue>
#include <stack>
#include <cmath>
#include <ctime>
#include <list>
#include <set>
#include <map>
//#include <tr1/unordered_set>
//#include <tr1/unordered_map>
//#include <array>
using namespace std;
#define REP(i, n) for (int i=0;i<n;++i)
#define FOR(i, a, b) for (int i=a;i<b;++i)
#define DWN(i, b, a) for (int i=b-1;i>=a;--i)
#define REP_1(i, n) for (int i=1;i<=n;++i)
#define FOR_1(i, a, b) for (int i=a;i<=b;++i)
#define DWN_1(i, b, a) for (int i=b;i>=a;--i)
#define REP_C(i, n) for (int n____=n,i=0;i<n____;++i)
#define FOR_C(i, a, b) for (int b____=b,i=a;i<b____;++i)
#define DWN_C(i, b, a) for (int a____=a,i=b-1;i>=a____;--i)
#define REP_N(i, n) for (i=0;i<n;++i)
#define FOR_N(i, a, b) for (i=a;i<b;++i)
#define DWN_N(i, b, a) for (i=b-1;i>=a;--i)
#define REP_1_C(i, n) for (int n____=n,i=1;i<=n____;++i)
#define FOR_1_C(i, a, b) for (int b____=b,i=a;i<=b____;++i)
#define DWN_1_C(i, b, a) for (int a____=a,i=b;i>=a____;--i)
#define REP_1_N(i, n) for (i=1;i<=n;++i)
#define FOR_1_N(i, a, b) for (i=a;i<=b;++i)
#define DWN_1_N(i, b, a) for (i=b;i>=a;--i)
#define REP_C_N(i, n) for (int n____=(i=0,n);i<n____;++i)
#define FOR_C_N(i, a, b) for (int b____=(i=0,b);i<b____;++i)
#define DWN_C_N(i, b, a) for (int a____=(i=b-1,a);i>=a____;--i)
#define REP_1_C_N(i, n) for (int n____=(i=1,n);i<=n____;++i)
#define FOR_1_C_N(i, a, b) for (int b____=(i=a,b);i<=b____;++i)
#define DWN_1_C_N(i, b, a) for (int a____=(i=b,a);i>=a____;--i)
#define ECH(it, A) for (__typeof(A.begin()) it=A.begin(); it != A.end(); ++it)
#define REP_S(i, str) for (char*i=str;*i;++i)
#define REP_L(i, hd, suc) for (int i=hd;i;i=suc[i])
#define REP_G(i, u) REP_L(i,hd[u],suc)
#define REP_SS(x, s) for (int x=s;x;x=(x-1)&s)
#define DO(n) for ( int ____n = n; ____n-->0; )
#define REP_2(i, j, n, m) REP(i, n) REP(j, m)
#define REP_2_1(i, j, n, m) REP_1(i, n) REP_1(j, m)
#define REP_3(i, j, k, n, m, l) REP(i, n) REP(j, m) REP(k, l)
#define REP_3_1(i, j, k, n, m, l) REP_1(i, n) REP_1(j, m) REP_1(k, l)
#define REP_4(i, j, k, ii, n, m, l, nn) REP(i, n) REP(j, m) REP(k, l) REP(ii, nn)
#define REP_4_1(i, j, k, ii, n, m, l, nn) REP_1(i, n) REP_1(j, m) REP_1(k, l) REP_1(ii, nn)
#define ALL(A) A.begin(), A.end()
#define LLA(A) A.rbegin(), A.rend()
#define CPY(A, B) memcpy(A, B, sizeof(A))
#define INS(A, P, B) A.insert(A.begin() + P, B)
#define ERS(A, P) A.erase(A.begin() + P)
#define LBD(A, x) (lower_bound(ALL(A), x) - A.begin())
#define UBD(A, x) (lower_bound(ALL(A), x) - A.begin())
#define CTN(T, x) (T.find(x) != T.end())
#define SZ(A) int((A).size())
#define PB push_back
#define MP(A, B) make_pair(A, B)
#define PTT pair<T, T>
#define Ts *this
#define rTs return Ts
#define fi first
#define se second
#define re real()
#define im imag()
#define Rush for(int ____T=RD(); ____T--;)
#define Display(A, n, m) { \
REP(i, n){ \
REP(j, m-1) cout << A[i][j] << " "; \
cout << A[i][m-1] << endl; \
} \
}
#define Display_1(A, n, m) { \
REP_1(i, n){ \
REP_1(j, m-1) cout << A[i][j] << " "; \
cout << A[i][m] << endl; \
} \
}
typedef long long LL;
//typedef long double DB;
typedef double DB;
typedef unsigned uint;
typedef unsigned long long uLL;
typedef vector<int> VI;
typedef vector<char> VC;
typedef vector<string> VS;
typedef vector<LL> VL;
typedef vector<DB> VF;
typedef set<int> SI;
typedef set<string> SS;
typedef map<int, int> MII;
typedef map<string, int> MSI;
typedef pair<int, int> PII;
typedef pair<LL, LL> PLL;
typedef vector<PII> VII;
typedef vector<VI> VVI;
typedef vector<VII> VVII;
template<class T> inline T& RD(T &);
template<class T> inline void OT(const T &);
//inline int RD(){int x; return RD(x);}
inline LL RD(){LL x; return RD(x);}
inline DB& RF(DB &);
inline DB RF(){DB x; return RF(x);}
inline char* RS(char *s);
inline char& RC(char &c);
inline char RC();
inline char& RC(char &c){scanf(" %c", &c); return c;}
inline char RC(){char c; return RC(c);}
//inline char& RC(char &c){c = getchar(); return c;}
//inline char RC(){return getchar();}
template<class T> inline T& RDD(T &);
inline LL RDD(){LL x; return RDD(x);}
template<class T0, class T1> inline T0& RD(T0 &x0, T1 &x1){RD(x0), RD(x1); return x0;}
template<class T0, class T1, class T2> inline T0& RD(T0 &x0, T1 &x1, T2 &x2){RD(x0), RD(x1), RD(x2); return x0;}
template<class T0, class T1, class T2, class T3> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3){RD(x0), RD(x1), RD(x2), RD(x3); return x0;}
template<class T0, class T1, class T2, class T3, class T4> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4); return x0;}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5); return x0;}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5, T6 &x6){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5), RD(x6); return x0;}
template<class T0, class T1> inline void OT(const T0 &x0, const T1 &x1){OT(x0), OT(x1);}
template<class T0, class T1, class T2> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2){OT(x0), OT(x1), OT(x2);}
template<class T0, class T1, class T2, class T3> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3){OT(x0), OT(x1), OT(x2), OT(x3);}
template<class T0, class T1, class T2, class T3, class T4> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3, const T4 &x4){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3, const T4 &x4, const T5 &x5){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3, const T4 &x4, const T5 &x5, const T6 &x6){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5), OT(x6);}
inline char& RC(char &a, char &b){RC(a), RC(b); return a;}
inline char& RC(char &a, char &b, char &c){RC(a), RC(b), RC(c); return a;}
inline char& RC(char &a, char &b, char &c, char &d){RC(a), RC(b), RC(c), RC(d); return a;}
inline char& RC(char &a, char &b, char &c, char &d, char &e){RC(a), RC(b), RC(c), RC(d), RC(e); return a;}
inline char& RC(char &a, char &b, char &c, char &d, char &e, char &f){RC(a), RC(b), RC(c), RC(d), RC(e), RC(f); return a;}
inline char& RC(char &a, char &b, char &c, char &d, char &e, char &f, char &g){RC(a), RC(b), RC(c), RC(d), RC(e), RC(f), RC(g); return a;}
inline DB& RF(DB &a, DB &b){RF(a), RF(b); return a;}
inline DB& RF(DB &a, DB &b, DB &c){RF(a), RF(b), RF(c); return a;}
inline DB& RF(DB &a, DB &b, DB &c, DB &d){RF(a), RF(b), RF(c), RF(d); return a;}
inline DB& RF(DB &a, DB &b, DB &c, DB &d, DB &e){RF(a), RF(b), RF(c), RF(d), RF(e); return a;}
inline DB& RF(DB &a, DB &b, DB &c, DB &d, DB &e, DB &f){RF(a), RF(b), RF(c), RF(d), RF(e), RF(f); return a;}
inline DB& RF(DB &a, DB &b, DB &c, DB &d, DB &e, DB &f, DB &g){RF(a), RF(b), RF(c), RF(d), RF(e), RF(f), RF(g); return a;}
inline void RS(char *s1, char *s2){RS(s1), RS(s2);}
inline void RS(char *s1, char *s2, char *s3){RS(s1), RS(s2), RS(s3);}
template<class T0,class T1>inline void RDD(T0&a, T1&b){RDD(a),RDD(b);}
template<class T0,class T1,class T2>inline void RDD(T0&a, T1&b, T2&c){RDD(a),RDD(b),RDD(c);}
template<class T> inline void RST(T &A){memset(A, 0, sizeof(A));}
template<class T> inline void FLC(T &A, int x){memset(A, x, sizeof(A));}
template<class T> inline void CLR(T &A){A.clear();}
template<class T0, class T1> inline void RST(T0 &A0, T1 &A1){RST(A0), RST(A1);}
template<class T0, class T1, class T2> inline void RST(T0 &A0, T1 &A1, T2 &A2){RST(A0), RST(A1), RST(A2);}
template<class T0, class T1, class T2, class T3> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3){RST(A0), RST(A1), RST(A2), RST(A3);}
template<class T0, class T1, class T2, class T3, class T4> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5), RST(A6);}
template<class T0, class T1> inline void FLC(T0 &A0, T1 &A1, int x){FLC(A0, x), FLC(A1, x);}
template<class T0, class T1, class T2> inline void FLC(T0 &A0, T1 &A1, T2 &A2, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x);}
template<class T0, class T1, class T2, class T3> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x);}
template<class T0, class T1, class T2, class T3, class T4> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x), FLC(A5, x);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x), FLC(A5, x), FLC(A6, x);}
template<class T> inline void CLR(priority_queue<T, vector<T>, less<T> > &Q){while (!Q.empty()) Q.pop();}
template<class T> inline void CLR(priority_queue<T, vector<T>, greater<T> > &Q){while (!Q.empty()) Q.pop();}
template<class T> inline void CLR(stack<T> &S){while (!S.empty()) S.pop();}
template<class T0, class T1> inline void CLR(T0 &A0, T1 &A1){CLR(A0), CLR(A1);}
template<class T0, class T1, class T2> inline void CLR(T0 &A0, T1 &A1, T2 &A2){CLR(A0), CLR(A1), CLR(A2);}
template<class T0, class T1, class T2, class T3> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3){CLR(A0), CLR(A1), CLR(A2), CLR(A3);}
template<class T0, class T1, class T2, class T3, class T4> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5), CLR(A6);}
template<class T> inline void CLR(T &A, int n){REP(i, n) CLR(A[i]);}
template<class T> inline bool EPT(T &a){return a.empty();}
template<class T> inline T& SRT(T &A){sort(ALL(A)); return A;}
template<class T, class C> inline T& SRT(T &A, C B){sort(ALL(A), B); return A;}
template<class T> inline T& RVS(T &A){reverse(ALL(A)); return A;}
template<class T> inline T& UNQQ(T &A){A.resize(unique(ALL(A))-A.begin());return A;}
template<class T> inline T& UNQ(T &A){SRT(A);return UNQQ(A);}
//}
/** Constant List .. **/ //{
const int MOD = int(1e9) + 7;
const int INF = 0x3f3f3f3f;
const LL INFF = 0x3f3f3f3f3f3f3f3fLL;
const DB EPS = 1e-9;
const DB OO = 1e20;
const DB PI = acos(-1.0); //M_PI;
const int dx[] = {-1, 0, 1, 0};
const int dy[] = {0, 1, 0, -1};
//}
/** Add On .. **/ //{
// <<= '0. Nichi Joo ., //{
template<class T> inline T& checkMin(T &a,const T b){if (b<a) a=b;return a;}
template<class T> inline T& checkMax(T &a,const T b){if (a<b) a=b;return a;}
template<class T> inline T& checkMin(T &a, T &b, const T x){checkMin(a, x), checkMin(b, x);return a;}
template<class T> inline T& checkMax(T &a, T &b, const T x){checkMax(a, x), checkMax(b, x);return a;}
template <class T, class C> inline T& checkMin(T& a, const T b, C c){if (c(b,a)) a = b;return a;}
template <class T, class C> inline T& checkMax(T& a, const T b, C c){if (c(a,b)) a = b;return a;}
template<class T> inline T min(T a, T b, T c){return min(min(a, b), c);}
template<class T> inline T max(T a, T b, T c){return max(max(a, b), c);}
template<class T> inline T min(T a, T b, T c, T d){return min(min(a, b), min(c, d));}
template<class T> inline T max(T a, T b, T c, T d){return max(max(a, b), max(c, d));}
template<class T> inline T min(T a, T b, T c, T d, T e){return min(min(min(a,b),min(c,d)),e);}
template<class T> inline T max(T a, T b, T c, T d, T e){return max(max(max(a,b),max(c,d)),e);}
template<class T> inline T sqr(T a){return a*a;}
template<class T> inline T cub(T a){return a*a*a;}
template<class T> inline T ceil(T x, T y){return (x - 1) / y + 1;}
template<class T> T abs(T x){return x>0?x:-x;}
inline int sgn(DB x){return x < -EPS ? -1 : x > EPS;}
inline int sgn(DB x, DB y){return sgn(x - y);}
inline DB cos(DB a, DB b, DB c){return (sqr(a)+sqr(b)-sqr(c))/(2*a*b);}
inline DB cot(DB x){return 1./tan(x);};
inline DB sec(DB x){return 1./cos(x);};
inline DB csc(DB x){return 1./sin(x);};
//}
// <<= '1. Bitwise Operation ., //{
namespace BO{
inline bool _1(int x, int i){return bool(x&1<<i);}
inline bool _1(LL x, int i){return bool(x&1LL<<i);}
inline LL _1(int i){return 1LL<<i;}
inline LL _U(int i){return _1(i) - 1;};
inline int reverse_bits(int x){
x = ((x >> 1) & 0x55555555) | ((x << 1) & 0xaaaaaaaa);
x = ((x >> 2) & 0x33333333) | ((x << 2) & 0xcccccccc);
x = ((x >> 4) & 0x0f0f0f0f) | ((x << 4) & 0xf0f0f0f0);
x = ((x >> 8) & 0x00ff00ff) | ((x << 8) & 0xff00ff00);
x = ((x >>16) & 0x0000ffff) | ((x <<16) & 0xffff0000);
return x;
}
inline LL reverse_bits(LL x){
x = ((x >> 1) & 0x5555555555555555LL) | ((x << 1) & 0xaaaaaaaaaaaaaaaaLL);
x = ((x >> 2) & 0x3333333333333333LL) | ((x << 2) & 0xccccccccccccccccLL);
x = ((x >> 4) & 0x0f0f0f0f0f0f0f0fLL) | ((x << 4) & 0xf0f0f0f0f0f0f0f0LL);
x = ((x >> 8) & 0x00ff00ff00ff00ffLL) | ((x << 8) & 0xff00ff00ff00ff00LL);
x = ((x >>16) & 0x0000ffff0000ffffLL) | ((x <<16) & 0xffff0000ffff0000LL);
x = ((x >>32) & 0x00000000ffffffffLL) | ((x <<32) & 0xffffffff00000000LL);
return x;
}
template<class T> inline bool odd(T x){return x&1;}
template<class T> inline bool even(T x){return !odd(x);}
template<class T> inline T low_bit(T x) {return x & -x;}
template<class T> inline T high_bit(T x) {T p = low_bit(x);while (p != x) x -= p, p = low_bit(x);return p;}
template<class T> inline T cover_bit(T x){T p = 1; while (p < x) p <<= 1;return p;}
template<class T> inline int cover_idx(T x){int p = 0; while (_1(p) < x ) ++p; return p;}
inline int clz(int x){return __builtin_clz(x);}
inline int clz(LL x){return __builtin_clzll(x);}
inline int ctz(int x){return __builtin_ctz(x);}
inline int ctz(LL x){return __builtin_ctzll(x);}
inline int lg2(int x){return !x ? -1 : 31 - clz(x);}
inline int lg2(LL x){return !x ? -1 : 63 - clz(x);}
inline int low_idx(int x){return !x ? -1 : ctz(x);}
inline int low_idx(LL x){return !x ? -1 : ctz(x);}
inline int high_idx(int x){return lg2(x);}
inline int high_idx(LL x){return lg2(x);}
inline int parity(int x){return __builtin_parity(x);}
inline int parity(LL x){return __builtin_parityll(x);}
inline int count_bits(int x){return __builtin_popcount(x);}
inline int count_bits(LL x){return __builtin_popcountll(x);}
} using namespace BO;//}
// <<= '2. Number Theory .,//{
namespace NT{
inline LL gcd(LL a, LL b){return __gcd(a, b);}
inline LL lcm(LL a, LL b){return a*b/gcd(a,b);}
inline void INC(int &a, int b){a += b; if (a >= MOD) a -= MOD;}
inline int sum(int a, int b){a += b; if (a >= MOD) a -= MOD; return a;}
inline void DEC(int &a, int b){a -= b; if (a < 0) a += MOD;}
inline int dff(int a, int b){a -= b; if (a < 0) a += MOD; return a;}
inline void MUL(int &a, int b){a = (LL)a * b % MOD;}
inline int pdt(int a, int b){return (LL)a * b % MOD;}
inline int gcd(int m, int n, int &x, int &y){
x = 1, y = 0; int xx = 0, yy = 1, q;
while (1){
q = m / n, m %= n;
if (!m){x = xx, y = yy; return n;}
DEC(x, pdt(q, xx)), DEC(y, pdt(q, yy));
q = n / m, n %= m;
if (!n) return m;
DEC(xx, pdt(q, x)), DEC(yy, pdt(q, y));
}
}
inline int sum(int a, int b, int c){return sum(a, sum(b, c));}
inline int sum(int a, int b, int c, int d){return sum(sum(a, b), sum(c, d));}
inline int pdt(int a, int b, int c){return pdt(a, pdt(b, c));}
inline int pdt(int a, int b, int c, int d){return pdt(pdt(a, b), pdt(c, d));}
inline int pow(int a, LL b){
int c(1); while (b){
if (b&1) MUL(c, a);
MUL(a, a), b >>= 1;
}
return c;
}
template<class T> inline T pow(T a, LL b){
T c(1); while (b){
if (b&1) c *= a;
a *= a, b >>= 1;
}
return c;
}
template<class T> inline T pow(T a, int b){
return pow(a, (LL)b);
}
inline int _I(int b){
int a = MOD, x1 = 0, x2 = 1, q;
while (true){
q = a / b, a %= b;
if (!a) return (x2 + MOD) % MOD;
DEC(x1, pdt(q, x2));
q = b / a, b %= a;
if (!b) return (x1 + MOD) % MOD;
DEC(x2, pdt(q, x1));
}
}
inline void DIV(int &a, int b){MUL(a, _I(b));}
inline int qtt(int a, int b){return pdt(a, _I(b));}
struct Int{
int val;
operator int() const{return val;}
Int(int val = 0):val(val){
val %= MOD; if (val < 0) val += MOD;
}
Int(LL _val){
_val %= MOD; if (_val < 0) _val += MOD;
val = _val;
}
Int& operator +=(const int& rhs){
INC(val, rhs);
return *this;
}
Int operator +(const int& rhs) const{
return sum(val, rhs);
}
Int& operator -=(const int& rhs){
DEC(val, rhs);
return *this;
}
Int operator -(const int& rhs) const{
return dff(val, rhs);
}
Int& operator *=(const int& rhs){
MUL(val, rhs);
return *this;
}
Int operator *(const int& rhs) const{
return pdt(val, rhs);
}
Int& operator /=(const int& rhs){
DIV(val, rhs);
return *this;
}
Int operator /(const int& rhs) const{
return qtt(val, rhs);
}
Int operator-()const{
return MOD-*this;
}
};
/*
Int Fact[N], Factt[N]; Int Binom(int n, int m){
return Fact[n] * Factt[m] * Factt[n-m];
}
*/
/*
Fact[0] = 1; REP_1(i, N-1) Fact[i] = Fact[i-1] * i;
Factt[N-1] = _I(Fact[N-1]); DWN(i, N, 1) Factt[i-1] = Factt[i] * i;
*/
/*
int Binom[N][N];
REP(i, N){Binom[i][0] = 1; REP_1(j, i) Binom[i][j] = Binom[i-1][j-1] + Binom[i-1][j];}
*/
/*
const int PMAX = 1;
VI P; bitset<PMAX> isP;
void sieve(){
FOR(i, 2, PMAX){
if (!isP[i]) P.PB(i);
for (int j=0;j<SZ(P)&&i*P[j]<PMAX;++j){
isP[i*P[j]]=1; if (!(i%P[j])) break;
}
}
}
*/
/*
inline int phi(int n){
int res = n; for (int i=2;sqr(i)<=n;++i) if (!(n%i)){
DEC(res, qtt(res, i));
do{n /= i;} while(!(n%i));
}
if (n != 1)
DEC(res, qtt(res, n));
return res;
}
*/
/*LL d, x, y; void exGcd(LL a, LL b){
if(!b) x = 1, y = 0, d = a;
else{
exGcd(b, a%b); LL t = y;
y = x - (a/b)*y, x = t;
}
}*/
} using namespace NT;//}
// <<= '9. Comutational Geometry .,//{
namespace CG{
#define cPo const Po&
#define cLine const Line&
#define cSeg const Seg&
inline DB dist2(DB x,DB y){return sqr(x)+sqr(y);}
struct Po{
DB x,y;Po(DB x=0,DB y=0):x(x),y(y){}
void in(){RF(x,y);}void out(){printf("(%.2f,%.2f)",x,y);}
inline friend istream&operator>>(istream&i,Po&p){return i>>p.x>>p.y;}
inline friend ostream&operator<<(ostream&o,Po p){return o<<"("<<p.x<<", "<<p.y<< ")";}
Po operator-()const{return Po(-x,-y);}
Po&operator+=(cPo p){x+=p.x,y+=p.y;rTs;}Po&operator-=(cPo p){x-=p.x,y-=p.y;rTs;}
Po&operator*=(DB k){x*=k,y*=k;rTs;}Po&operator/=(DB k){x/=k,y/=k;rTs;}
Po&operator*=(cPo p){rTs=Ts*p;}Po&operator/=(cPo p){rTs=Ts/p;}
Po operator+(cPo p)const{return Po(x+p.x,y+p.y);}Po operator-(cPo p)const{return Po(x-p.x,y-p.y);}
Po operator*(DB k)const{return Po(x*k,y*k);}Po operator/(DB k)const{return Po(x/k,y/k);}
Po operator*(cPo p)const{return Po(x*p.x-y*p.y,y*p.x+x*p.y);}Po operator/(cPo p)const{return Po(x*p.x+y*p.y,y*p.x-x*p.y)/p.len2();}
bool operator==(cPo p)const{return!sgn(x,p.x)&&!sgn(y,p.y);};bool operator!=(cPo p)const{return sgn(x,p.x)||sgn(y,p.y);}
bool operator<(cPo p)const{return sgn(x,p.x)<0||!sgn(x,p.x)&&sgn(y,p.y)<0;}bool operator<=(cPo p)const{return sgn(x,p.x)<0||!sgn(x,p.x)&&sgn(y,p.y)<=0;}
bool operator>(cPo p)const{return!(Ts<=p);}bool operator >=(cPo p)const{return!(Ts<p);}
DB len2()const{return dist2(x,y);}DB len()const{return sqrt(len2());}DB arg()const{return atan2(y,x);}
Po&_1(){rTs/=len();}Po&conj(){y=-y;rTs;}Po&lt(){swap(x,y),x=-x;rTs;}Po&rt(){swap(x,y),y=-y;rTs;}
Po&rot(DB a,cPo o=Po()){Ts-=o;Ts*=Po(cos(a),sin(a));rTs+=o;}
};
inline DB dot(DB x1,DB y1,DB x2,DB y2){return x1*x2+y1*y2;}
inline DB dot(cPo a,cPo b){return dot(a.x,a.y,b.x,b.y);}
inline DB dot(cPo p0,cPo p1,cPo p2){return dot(p1-p0,p2-p0);}
inline DB det(DB x1,DB y1,DB x2,DB y2){return x1*y2-x2*y1;}
inline DB det(cPo a,cPo b){return det(a.x,a.y,b.x,b.y);}
inline DB det(cPo p0,cPo p1,cPo p2){return det(p1-p0,p2-p0);}
inline DB ang(cPo p0,cPo p1){return acos(dot(p0,p1)/p0.len()/p1.len());}
inline DB ang(cPo p0,cPo p1,cPo p2){return ang(p1-p0,p2-p0);}
inline DB ang(cPo p0,cPo p1,cPo p2,cPo p3){return ang(p1-p0,p3-p2);}
inline DB dist2(const Po &a, const Po &b){return dist2(a.x-b.x, a.y-b.y);}
template<class T1, class T2> inline int dett(const T1 &x, const T2 &y){return sgn(det(x, y));}
template<class T1, class T2, class T3> inline int dett(const T1 &x, const T2 &y, const T3 &z){return sgn(det(x, y, z));}
template<class T1, class T2, class T3, class T4> inline int dett(const T1 &x, const T2 &y, const T3 &z, const T4 &w){return sgn(det(x, y, z, w));}
template<class T1, class T2> inline int dott(const T1 &x, const T2 &y){return sgn(dot(x, y));}
template<class T1, class T2, class T3> inline int dott(const T1 &x, const T2 &y, const T3 &z){return sgn(dot(x, y, z));}
template<class T1, class T2, class T3, class T4> inline int dott(const T1 &x, const T2 &y, const T3 &z, const T4 &w){return sgn(dot(x, y, z, w));}
template<class T1, class T2> inline DB arg(const T1 &x, const T2 &y){DB a=ang(x,y);return~dett(x,y)?a:2*PI-a;}
template<class T1, class T2, class T3> inline DB arg(const T1 &x, const T2 &y, const T3 &z){DB a=ang(x,y,z);return~dett(x,y,z)?a:2*PI-a;}
template<class T1, class T2, class T3, class T4> inline DB arg(const T1 &x, const T2 &y, const T3 &z, const T4 &w){DB a=ang(x,y,z,w);return~dett(x,y,z,w)?a:2*PI-a;}
template<class T1, class T2> inline DB dist(const T1 &x, const T2 &y){return sqrt(dist2(x, y));}
template<class T1, class T2, class T3> inline DB dist(const T1 &x, const T2 &y, const T3 &z){return sqrt(dist2(x, y, z));}
inline Po _1(Po p){return p._1();}inline Po conj(Po p){return p.conj();}
inline Po lt(Po p){return p.lt();}inline Po rt(Po p){return p.rt();}
inline Po rot(Po p,DB a,cPo o=Po()){return p.rot(a,o);}
inline Po operator *(DB k,cPo p){return p*k;}
inline Po operator /(DB k,cPo p){return conj(p)*k/p.len2();}
typedef vector<Po> VP;
struct Line{
Po a,b;Line(cPo a=Po(),cPo b=Po()):a(a),b(b){}
Line(DB x0,DB y0,DB x1,DB y1):a(Po(x0,y0)),b(Po(x1,y1)){}
Line(cLine l):a(l.a),b(l.b){}
//Ax+By+C=0
Line(DB A,DB B,DB C){
C=-C;if(!::sgn(A))a=Po(0,C/B),b=Po(1,C/B);
else if(!::sgn(B))a=Po(C/A,0),b=Po(C/A,1);
else a=Po(0,C/B),b=Po(1,(C-A)/B);
}
void in(){a.in(),b.in();}
inline friend istream&operator>>(istream&i,Line& p){return i>>p.a>>p.b;}
inline friend ostream&operator<<(ostream&o,Line p){return o<<p.a<<"-"<< p.b;}
Line operator+(cPo x)const{return Line(a+x,b+x);}
Line operator-(cPo x)const{return Line(a-x,b-x);}
Line operator*(DB k)const{return Line(a*k,b*k);}
Line operator/(DB k)const{return Line(a/k,b/k);}
Po operator*(cLine)const;
Po d()const{return b-a;}DB len2()const{return d().len2();}DB len()const{return d().len();}DB arg()const{return d().arg();}
int sgn(cPo p)const{return dett(a, b, p);}
int sgn(cLine)const;
bool sameSgn(cPo p1,cPo p2)const{return sgn(p1)==sgn(p2);}
void getEquation(DB&K,DB&B)const{
K = ::sgn(a.x, b.x) ? (b.y-a.y)/(b.x-a.x) : OO;
B = a.y - K*a.x;
}
void getEquation(DB&A,DB&B,DB&C)const{A=a.y-b.y,B=b.x-a.x,C=det(a, b);}
Line&push(DB r){ // 正数右手螺旋向里
Po v=d()._1().lt()*r;a+=v,b+=v; rTs;
}
};
inline DB dot(cLine l1,cLine l2){return dot(l1.d(),l2.d());}
inline DB dot(cLine l,cPo p){return dot(l.a,l.b,p);}
inline DB dot(cPo p,cLine l){return dot(p,l.a,l.b);}
inline DB det(cLine l1,cLine l2){return det(l1.d(),l2.d());}
inline DB det(cLine l,cPo p){return det(l.a,l.b,p);}
inline DB det(cPo p,cLine l){return det(p,l.a,l.b);}
inline DB ang(cLine l0,cLine l1){return ang(l0.d(),l1.d());}
inline DB ang(cLine l,cPo p){return ang(l.a,l.b,p);}
inline DB ang(cPo p,cLine l){return ang(p,l.a,l.b);}
inline int Line::sgn(cLine l)const{return dett(Ts, l);}
inline Po Line::operator*(cLine l)const{return a+d()*det(a,l)/det(Ts,l);}
inline Po operator&(cPo p,cLine l){return l*Line(p,p+l.d().lt());}
inline Po operator%(cPo p,cLine l){return p&l*2-p;}
inline Line push(Line l, DB r){return l.push(r);}
struct Seg: public Line{
Seg(cPo a=Po(),cPo b=Po()):Line(a,b){}
Seg(DB x0,DB y0,DB x1,DB y1):Line(x0,y0,x1,y1){}
Seg(cLine l):Line(l){}
Seg(const Po &a,DB alpha):Line(a,alpha){}
Seg(DB A,DB B,DB C):Line(A,B,C){}
inline int sgn(cPo p)const;
inline int sgn(cLine l)const;
inline bool qrt(cSeg l)const;
inline int sgn(cSeg l)const;
};
// -1不相交 0相交（不规范） 1相交（规范）
inline int Seg::sgn(cPo p)const{return -dott(p,a,b);}
inline int Seg::sgn(cLine l)const{return sgn(Ts*l);}
// quick_rejection_test
inline bool Seg::qrt(cSeg l)const{
return min(a.x,b.x)<=max(l.a.x,l.b.x)&&min(l.a.x,l.b.x)<=max(a.x,b.x)&&
min(a.y,b.y)<=max(l.a.y,l.b.y)&&min(l.a.y,l.b.y)<=max(a.y,b.y);
}
inline int Seg::sgn(cSeg l)const{
if (!qrt(l)) return -1;
/*return
(dett(a,b,l.a)*dett(a,b,l.b)<=0 &&
dett(l.a,l.b,a)*dett(l.a,l.b,b)<=0)?1:-1;*/
int d1=dett(a,b,l.a),d2=dett(a,b,l.b),d3=dett(l.a,l.b,a),d4=dett(l.a,l.b,b);
if ((d1^d2)==-2&&(d3^d4)==-2)return 1;
return ((!d1&&dott(l.a-a,l.a-b)<=0)||(!d2&&dott(l.b-a,l.b-b)<=0)||
(!d3&&dott(a-l.a,a-l.b)<=0)||(!d4&&dott(b-l.a,b-l.b)<=0))?0:-1;
}
//inline DB dist2(cLine l,cPo p){return sqr(fabs(dot(lt(l.d()), p-l.a)))/l.len2();}
inline DB dist2(cLine l,cPo p){return sqr(fabs(det(l.d(), p-l.a)))/l.len2();}
inline DB dist2(cLine l1,cLine l2){return dett(l1,l2)?0:dist2(l1,l2.a);}
inline DB dist2(cSeg l,cPo p){
Po pa = p - l.a, pb = p - l.b;
if (dott(l.d(), pa) <= 0) return pa.len2();
if (dott(l.d(), pb) >= 0) return pb.len2();
return dist2(Line(l), p);
}
inline DB dist2(cSeg s,cLine l){
Po v1=s.a-l.a,v2=s.b-l.a;DB d1=det(l.d(),v1),d2=det(l.d(),v2);
return sgn(d1)!=sgn(d2) ? 0 : sqr(min(fabs(d1), fabs(d2)))/l.len2();
}
inline DB dist2(cSeg l1,cSeg l2){
if (~l1.sgn(l2)) return 0;
else return min(dist2(l2,l1.a), dist2(l2,l1.b), dist2(l1,l2.a), dist2(l1,l2.b));
}
template<class T1, class T2> inline DB dist2(const T1& a, const T2& b){
return dist2(b, a);
}
Po getPo(){Po p;p.in();return p;}
Line getLine(){Line l;l.in();return l;}
DB getArea(const VP& P){DB z=0;FOR(i,1,SZ(P))z+=det(P[i-1],P[i]);return z;}
DB getPeri(const VP& P){DB z=0;FOR(i,1,SZ(P))z+=dist(P[i-1],P[i]);return z;}
} using namespace CG;//}
//}
/** I/O Accelerator Interface .. **/ //{
#define g (c=getchar())
#define d isdigit(g)
#define p x=x*10+c-'0'
#define n x=x*10+'0'-c
#define pp l/=10,p
#define nn l/=10,n
template<class T> inline T& RD(T &x){
char c;while(!d);x=c-'0';while(d)p;
return x;
}
template<class T> inline T& RDD(T &x){
char c;while(g,c!='-'&&!isdigit(c));
if (c=='-'){x='0'-g;while(d)n;}
else{x=c-'0';while(d)p;}
return x;
}
inline DB& RF(DB &x){
//scanf("%lf", &x);
char c;while(g,c!='-'&&c!='.'&&!isdigit(c));
if(c=='-')if(g=='.'){x=0;DB l=1;while(d)nn;x*=l;}
else{x='0'-c;while(d)n;if(c=='.'){DB l=1;while(d)nn;x*=l;}}
else if(c=='.'){x=0;DB l=1;while(d)pp;x*=l;}
else{x=c-'0';while(d)p;if(c=='.'){DB l=1;while(d)pp;x*=l;}}
return x;
}
#undef nn
#undef pp
#undef n
#undef p
#undef d
#undef g
inline char* RS(char *s){
//gets(s);
scanf("%s", s);
return s;
}
LL last_ans; int Case; template<class T> inline void OT(const T &x){
//printf("Case #%d: ", ++Case);
//printf("%lld\n", x);
//printf("%.3f\n", x);
printf("%d\n", x);
//cout << x << endl;
//last_ans = x;
}
//}
//}/* .................................................................................................................................. */
const int N = 40, M = N*1000+1;
DB dp[M]; int n; DB p;
int main(){
#ifndef ONLINE_JUDGE
freopen("in.txt", "r", stdin);
//freopen("out.txt", "w", stdout);
#endif
Rush{
RST(dp); dp[0] = 1; int m = 0;
RD(n); RF(p); REP(i, n){
int a; m += RD(a); DWN_1(i, m, 0) dp[i] = dp[i]/2 + (i-a>=0?dp[i-a]/2:0);
}
DB s=0; REP(i, M) if (~sgn(s += dp[i], p)){
OT(i); break;
}
}
}
Raw
D.cpp
/** Micro Mezz Macro Flation -- Overheated Economy ., Last Update: May. 7th 2014 **/ //{
/** Header .. **/ //{
#pragma comment(linker, "/STACK:36777216")
//#pragma GCC optimize ("O2")
#define LOCAL
//#include "testlib.h"
#include <functional>
#include <algorithm>
#include <iostream>
#include <fstream>
#include <sstream>
#include <iomanip>
#include <numeric>
#include <cstring>
#include <climits>
#include <cassert>
#include <complex>
#include <cstdio>
#include <string>
#include <vector>
#include <bitset>
#include <queue>
#include <stack>
#include <cmath>
#include <ctime>
#include <list>
#include <set>
#include <map>
//#include <tr1/unordered_set>
//#include <tr1/unordered_map>
//#include <array>
using namespace std;
#define REP(i, n) for (int i=0;i<n;++i)
#define FOR(i, a, b) for (int i=a;i<b;++i)
#define DWN(i, b, a) for (int i=b-1;i>=a;--i)
#define REP_1(i, n) for (int i=1;i<=n;++i)
#define FOR_1(i, a, b) for (int i=a;i<=b;++i)
#define DWN_1(i, b, a) for (int i=b;i>=a;--i)
#define REP_C(i, n) for (int n____=n,i=0;i<n____;++i)
#define FOR_C(i, a, b) for (int b____=b,i=a;i<b____;++i)
#define DWN_C(i, b, a) for (int a____=a,i=b-1;i>=a____;--i)
#define REP_N(i, n) for (i=0;i<n;++i)
#define FOR_N(i, a, b) for (i=a;i<b;++i)
#define DWN_N(i, b, a) for (i=b-1;i>=a;--i)
#define REP_1_C(i, n) for (int n____=n,i=1;i<=n____;++i)
#define FOR_1_C(i, a, b) for (int b____=b,i=a;i<=b____;++i)
#define DWN_1_C(i, b, a) for (int a____=a,i=b;i>=a____;--i)
#define REP_1_N(i, n) for (i=1;i<=n;++i)
#define FOR_1_N(i, a, b) for (i=a;i<=b;++i)
#define DWN_1_N(i, b, a) for (i=b;i>=a;--i)
#define REP_C_N(i, n) for (int n____=(i=0,n);i<n____;++i)
#define FOR_C_N(i, a, b) for (int b____=(i=0,b);i<b____;++i)
#define DWN_C_N(i, b, a) for (int a____=(i=b-1,a);i>=a____;--i)
#define REP_1_C_N(i, n) for (int n____=(i=1,n);i<=n____;++i)
#define FOR_1_C_N(i, a, b) for (int b____=(i=a,b);i<=b____;++i)
#define DWN_1_C_N(i, b, a) for (int a____=(i=b,a);i>=a____;--i)
#define ECH(it, A) for (__typeof(A.begin()) it=A.begin(); it != A.end(); ++it)
#define REP_S(i, str) for (char*i=str;*i;++i)
#define REP_L(i, hd, suc) for (int i=hd;i;i=suc[i])
#define REP_G(i, u) REP_L(i,hd[u],suc)
#define REP_SS(x, s) for (int x=s;x;x=(x-1)&s)
#define DO(n) for ( int ____n = n; ____n-->0; )
#define REP_2(i, j, n, m) REP(i, n) REP(j, m)
#define REP_2_1(i, j, n, m) REP_1(i, n) REP_1(j, m)
#define REP_3(i, j, k, n, m, l) REP(i, n) REP(j, m) REP(k, l)
#define REP_3_1(i, j, k, n, m, l) REP_1(i, n) REP_1(j, m) REP_1(k, l)
#define REP_4(i, j, k, ii, n, m, l, nn) REP(i, n) REP(j, m) REP(k, l) REP(ii, nn)
#define REP_4_1(i, j, k, ii, n, m, l, nn) REP_1(i, n) REP_1(j, m) REP_1(k, l) REP_1(ii, nn)
#define ALL(A) A.begin(), A.end()
#define LLA(A) A.rbegin(), A.rend()
#define CPY(A, B) memcpy(A, B, sizeof(A))
#define INS(A, P, B) A.insert(A.begin() + P, B)
#define ERS(A, P) A.erase(A.begin() + P)
#define LBD(A, x) (lower_bound(ALL(A), x) - A.begin())
#define UBD(A, x) (lower_bound(ALL(A), x) - A.begin())
#define CTN(T, x) (T.find(x) != T.end())
#define SZ(A) int((A).size())
#define PB push_back
#define MP(A, B) make_pair(A, B)
#define PTT pair<T, T>
#define Ts *this
#define rTs return Ts
#define fi first
#define se second
#define re real()
#define im imag()
#define Rush for(int ____T=RD(); ____T--;)
#define Display(A, n, m) { \
REP(i, n){ \
REP(j, m-1) cout << A[i][j] << " "; \
cout << A[i][m-1] << endl; \
} \
}
#define Display_1(A, n, m) { \
REP_1(i, n){ \
REP_1(j, m-1) cout << A[i][j] << " "; \
cout << A[i][m] << endl; \
} \
}
typedef long long LL;
//typedef long double DB;
typedef double DB;
typedef unsigned uint;
typedef unsigned long long uLL;
typedef vector<int> VI;
typedef vector<char> VC;
typedef vector<string> VS;
typedef vector<LL> VL;
typedef vector<DB> VF;
typedef set<int> SI;
typedef set<string> SS;
typedef map<int, int> MII;
typedef map<string, int> MSI;
typedef pair<int, int> PII;
typedef pair<LL, LL> PLL;
typedef vector<PII> VII;
typedef vector<VI> VVI;
typedef vector<VII> VVII;
template<class T> inline T& RD(T &);
template<class T> inline void OT(const T &);
//inline int RD(){int x; return RD(x);}
inline LL RD(){LL x; return RD(x);}
inline DB& RF(DB &);
inline DB RF(){DB x; return RF(x);}
inline char* RS(char *s);
inline char& RC(char &c);
inline char RC();
inline char& RC(char &c){scanf(" %c", &c); return c;}
inline char RC(){char c; return RC(c);}
//inline char& RC(char &c){c = getchar(); return c;}
//inline char RC(){return getchar();}
template<class T> inline T& RDD(T &);
inline LL RDD(){LL x; return RDD(x);}
template<class T0, class T1> inline T0& RD(T0 &x0, T1 &x1){RD(x0), RD(x1); return x0;}
template<class T0, class T1, class T2> inline T0& RD(T0 &x0, T1 &x1, T2 &x2){RD(x0), RD(x1), RD(x2); return x0;}
template<class T0, class T1, class T2, class T3> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3){RD(x0), RD(x1), RD(x2), RD(x3); return x0;}
template<class T0, class T1, class T2, class T3, class T4> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4); return x0;}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5); return x0;}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5, T6 &x6){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5), RD(x6); return x0;}
template<class T0, class T1> inline void OT(const T0 &x0, const T1 &x1){OT(x0), OT(x1);}
template<class T0, class T1, class T2> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2){OT(x0), OT(x1), OT(x2);}
template<class T0, class T1, class T2, class T3> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3){OT(x0), OT(x1), OT(x2), OT(x3);}
template<class T0, class T1, class T2, class T3, class T4> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3, const T4 &x4){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3, const T4 &x4, const T5 &x5){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3, const T4 &x4, const T5 &x5, const T6 &x6){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5), OT(x6);}
inline char& RC(char &a, char &b){RC(a), RC(b); return a;}
inline char& RC(char &a, char &b, char &c){RC(a), RC(b), RC(c); return a;}
inline char& RC(char &a, char &b, char &c, char &d){RC(a), RC(b), RC(c), RC(d); return a;}
inline char& RC(char &a, char &b, char &c, char &d, char &e){RC(a), RC(b), RC(c), RC(d), RC(e); return a;}
inline char& RC(char &a, char &b, char &c, char &d, char &e, char &f){RC(a), RC(b), RC(c), RC(d), RC(e), RC(f); return a;}
inline char& RC(char &a, char &b, char &c, char &d, char &e, char &f, char &g){RC(a), RC(b), RC(c), RC(d), RC(e), RC(f), RC(g); return a;}
inline DB& RF(DB &a, DB &b){RF(a), RF(b); return a;}
inline DB& RF(DB &a, DB &b, DB &c){RF(a), RF(b), RF(c); return a;}
inline DB& RF(DB &a, DB &b, DB &c, DB &d){RF(a), RF(b), RF(c), RF(d); return a;}
inline DB& RF(DB &a, DB &b, DB &c, DB &d, DB &e){RF(a), RF(b), RF(c), RF(d), RF(e); return a;}
inline DB& RF(DB &a, DB &b, DB &c, DB &d, DB &e, DB &f){RF(a), RF(b), RF(c), RF(d), RF(e), RF(f); return a;}
inline DB& RF(DB &a, DB &b, DB &c, DB &d, DB &e, DB &f, DB &g){RF(a), RF(b), RF(c), RF(d), RF(e), RF(f), RF(g); return a;}
inline void RS(char *s1, char *s2){RS(s1), RS(s2);}
inline void RS(char *s1, char *s2, char *s3){RS(s1), RS(s2), RS(s3);}
template<class T0,class T1>inline void RDD(T0&a, T1&b){RDD(a),RDD(b);}
template<class T0,class T1,class T2>inline void RDD(T0&a, T1&b, T2&c){RDD(a),RDD(b),RDD(c);}
template<class T> inline void RST(T &A){memset(A, 0, sizeof(A));}
template<class T> inline void FLC(T &A, int x){memset(A, x, sizeof(A));}
template<class T> inline void CLR(T &A){A.clear();}
template<class T0, class T1> inline void RST(T0 &A0, T1 &A1){RST(A0), RST(A1);}
template<class T0, class T1, class T2> inline void RST(T0 &A0, T1 &A1, T2 &A2){RST(A0), RST(A1), RST(A2);}
template<class T0, class T1, class T2, class T3> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3){RST(A0), RST(A1), RST(A2), RST(A3);}
template<class T0, class T1, class T2, class T3, class T4> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5), RST(A6);}
template<class T0, class T1> inline void FLC(T0 &A0, T1 &A1, int x){FLC(A0, x), FLC(A1, x);}
template<class T0, class T1, class T2> inline void FLC(T0 &A0, T1 &A1, T2 &A2, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x);}
template<class T0, class T1, class T2, class T3> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x);}
template<class T0, class T1, class T2, class T3, class T4> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x), FLC(A5, x);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x), FLC(A5, x), FLC(A6, x);}
template<class T> inline void CLR(priority_queue<T, vector<T>, less<T> > &Q){while (!Q.empty()) Q.pop();}
template<class T> inline void CLR(priority_queue<T, vector<T>, greater<T> > &Q){while (!Q.empty()) Q.pop();}
template<class T> inline void CLR(stack<T> &S){while (!S.empty()) S.pop();}
template<class T0, class T1> inline void CLR(T0 &A0, T1 &A1){CLR(A0), CLR(A1);}
template<class T0, class T1, class T2> inline void CLR(T0 &A0, T1 &A1, T2 &A2){CLR(A0), CLR(A1), CLR(A2);}
template<class T0, class T1, class T2, class T3> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3){CLR(A0), CLR(A1), CLR(A2), CLR(A3);}
template<class T0, class T1, class T2, class T3, class T4> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5), CLR(A6);}
template<class T> inline void CLR(T &A, int n){REP(i, n) CLR(A[i]);}
template<class T> inline bool EPT(T &a){return a.empty();}
template<class T> inline T& SRT(T &A){sort(ALL(A)); return A;}
template<class T, class C> inline T& SRT(T &A, C B){sort(ALL(A), B); return A;}
template<class T> inline T& RVS(T &A){reverse(ALL(A)); return A;}
template<class T> inline T& UNQQ(T &A){A.resize(unique(ALL(A))-A.begin());return A;}
template<class T> inline T& UNQ(T &A){SRT(A);return UNQQ(A);}
//}
/** Constant List .. **/ //{
const int MOD = int(1e9) + 7;
const int INF = 0x3f3f3f3f;
const LL INFF = 0x3f3f3f3f3f3f3f3fLL;
const DB EPS = 1e-9;
const DB OO = 1e20;
const DB PI = acos(-1.0); //M_PI;
const int dx[] = {-1, 0, 1, 0};
const int dy[] = {0, 1, 0, -1};
//}
/** Add On .. **/ //{
// <<= '0. Nichi Joo ., //{
template<class T> inline T& checkMin(T &a,const T b){if (b<a) a=b;return a;}
template<class T> inline T& checkMax(T &a,const T b){if (a<b) a=b;return a;}
template<class T> inline T& checkMin(T &a, T &b, const T x){checkMin(a, x), checkMin(b, x);return a;}
template<class T> inline T& checkMax(T &a, T &b, const T x){checkMax(a, x), checkMax(b, x);return a;}
template <class T, class C> inline T& checkMin(T& a, const T b, C c){if (c(b,a)) a = b;return a;}
template <class T, class C> inline T& checkMax(T& a, const T b, C c){if (c(a,b)) a = b;return a;}
template<class T> inline T min(T a, T b, T c){return min(min(a, b), c);}
template<class T> inline T max(T a, T b, T c){return max(max(a, b), c);}
template<class T> inline T min(T a, T b, T c, T d){return min(min(a, b), min(c, d));}
template<class T> inline T max(T a, T b, T c, T d){return max(max(a, b), max(c, d));}
template<class T> inline T min(T a, T b, T c, T d, T e){return min(min(min(a,b),min(c,d)),e);}
template<class T> inline T max(T a, T b, T c, T d, T e){return max(max(max(a,b),max(c,d)),e);}
template<class T> inline T sqr(T a){return a*a;}
template<class T> inline T cub(T a){return a*a*a;}
template<class T> inline T ceil(T x, T y){return (x - 1) / y + 1;}
template<class T> T abs(T x){return x>0?x:-x;}
inline int sgn(DB x){return x < -EPS ? -1 : x > EPS;}
inline int sgn(DB x, DB y){return sgn(x - y);}
inline DB cos(DB a, DB b, DB c){return (sqr(a)+sqr(b)-sqr(c))/(2*a*b);}
inline DB cot(DB x){return 1./tan(x);};
inline DB sec(DB x){return 1./cos(x);};
inline DB csc(DB x){return 1./sin(x);};
//}
// <<= '1. Bitwise Operation ., //{
namespace BO{
inline bool _1(int x, int i){return bool(x&1<<i);}
inline bool _1(LL x, int i){return bool(x&1LL<<i);}
inline LL _1(int i){return 1LL<<i;}
inline LL _U(int i){return _1(i) - 1;};
inline int reverse_bits(int x){
x = ((x >> 1) & 0x55555555) | ((x << 1) & 0xaaaaaaaa);
x = ((x >> 2) & 0x33333333) | ((x << 2) & 0xcccccccc);
x = ((x >> 4) & 0x0f0f0f0f) | ((x << 4) & 0xf0f0f0f0);
x = ((x >> 8) & 0x00ff00ff) | ((x << 8) & 0xff00ff00);
x = ((x >>16) & 0x0000ffff) | ((x <<16) & 0xffff0000);
return x;
}
inline LL reverse_bits(LL x){
x = ((x >> 1) & 0x5555555555555555LL) | ((x << 1) & 0xaaaaaaaaaaaaaaaaLL);
x = ((x >> 2) & 0x3333333333333333LL) | ((x << 2) & 0xccccccccccccccccLL);
x = ((x >> 4) & 0x0f0f0f0f0f0f0f0fLL) | ((x << 4) & 0xf0f0f0f0f0f0f0f0LL);
x = ((x >> 8) & 0x00ff00ff00ff00ffLL) | ((x << 8) & 0xff00ff00ff00ff00LL);
x = ((x >>16) & 0x0000ffff0000ffffLL) | ((x <<16) & 0xffff0000ffff0000LL);
x = ((x >>32) & 0x00000000ffffffffLL) | ((x <<32) & 0xffffffff00000000LL);
return x;
}
template<class T> inline bool odd(T x){return x&1;}
template<class T> inline bool even(T x){return !odd(x);}
template<class T> inline T low_bit(T x) {return x & -x;}
template<class T> inline T high_bit(T x) {T p = low_bit(x);while (p != x) x -= p, p = low_bit(x);return p;}
template<class T> inline T cover_bit(T x){T p = 1; while (p < x) p <<= 1;return p;}
template<class T> inline int cover_idx(T x){int p = 0; while (_1(p) < x ) ++p; return p;}
inline int clz(int x){return __builtin_clz(x);}
inline int clz(LL x){return __builtin_clzll(x);}
inline int ctz(int x){return __builtin_ctz(x);}
inline int ctz(LL x){return __builtin_ctzll(x);}
inline int lg2(int x){return !x ? -1 : 31 - clz(x);}
inline int lg2(LL x){return !x ? -1 : 63 - clz(x);}
inline int low_idx(int x){return !x ? -1 : ctz(x);}
inline int low_idx(LL x){return !x ? -1 : ctz(x);}
inline int high_idx(int x){return lg2(x);}
inline int high_idx(LL x){return lg2(x);}
inline int parity(int x){return __builtin_parity(x);}
inline int parity(LL x){return __builtin_parityll(x);}
inline int count_bits(int x){return __builtin_popcount(x);}
inline int count_bits(LL x){return __builtin_popcountll(x);}
} using namespace BO;//}
// <<= '2. Number Theory .,//{
namespace NT{
inline LL gcd(LL a, LL b){return __gcd(a, b);}
inline LL lcm(LL a, LL b){return a*b/gcd(a,b);}
inline void INC(int &a, int b){a += b; if (a >= MOD) a -= MOD;}
inline int sum(int a, int b){a += b; if (a >= MOD) a -= MOD; return a;}
inline void DEC(int &a, int b){a -= b; if (a < 0) a += MOD;}
inline int dff(int a, int b){a -= b; if (a < 0) a += MOD; return a;}
inline void MUL(int &a, int b){a = (LL)a * b % MOD;}
inline int pdt(int a, int b){return (LL)a * b % MOD;}
inline int gcd(int m, int n, int &x, int &y){
x = 1, y = 0; int xx = 0, yy = 1, q;
while (1){
q = m / n, m %= n;
if (!m){x = xx, y = yy; return n;}
DEC(x, pdt(q, xx)), DEC(y, pdt(q, yy));
q = n / m, n %= m;
if (!n) return m;
DEC(xx, pdt(q, x)), DEC(yy, pdt(q, y));
}
}
inline int sum(int a, int b, int c){return sum(a, sum(b, c));}
inline int sum(int a, int b, int c, int d){return sum(sum(a, b), sum(c, d));}
inline int pdt(int a, int b, int c){return pdt(a, pdt(b, c));}
inline int pdt(int a, int b, int c, int d){return pdt(pdt(a, b), pdt(c, d));}
inline int pow(int a, LL b){
int c(1); while (b){
if (b&1) MUL(c, a);
MUL(a, a), b >>= 1;
}
return c;
}
template<class T> inline T pow(T a, LL b){
T c(1); while (b){
if (b&1) c *= a;
a *= a, b >>= 1;
}
return c;
}
template<class T> inline T pow(T a, int b){
return pow(a, (LL)b);
}
inline int _I(int b){
int a = MOD, x1 = 0, x2 = 1, q;
while (true){
q = a / b, a %= b;
if (!a) return (x2 + MOD) % MOD;
DEC(x1, pdt(q, x2));
q = b / a, b %= a;
if (!b) return (x1 + MOD) % MOD;
DEC(x2, pdt(q, x1));
}
}
inline void DIV(int &a, int b){MUL(a, _I(b));}
inline int qtt(int a, int b){return pdt(a, _I(b));}
struct Int{
int val;
operator int() const{return val;}
Int(int val = 0):val(val){
val %= MOD; if (val < 0) val += MOD;
}
Int(LL _val){
_val %= MOD; if (_val < 0) _val += MOD;
val = _val;
}
Int& operator +=(const int& rhs){
INC(val, rhs);
return *this;
}
Int operator +(const int& rhs) const{
return sum(val, rhs);
}
Int& operator -=(const int& rhs){
DEC(val, rhs);
return *this;
}
Int operator -(const int& rhs) const{
return dff(val, rhs);
}
Int& operator *=(const int& rhs){
MUL(val, rhs);
return *this;
}
Int operator *(const int& rhs) const{
return pdt(val, rhs);
}
Int& operator /=(const int& rhs){
DIV(val, rhs);
return *this;
}
Int operator /(const int& rhs) const{
return qtt(val, rhs);
}
Int operator-()const{
return MOD-*this;
}
};
/*
Int Fact[N], Factt[N]; Int Binom(int n, int m){
return Fact[n] * Factt[m] * Factt[n-m];
}
*/
/*
Fact[0] = 1; REP_1(i, N-1) Fact[i] = Fact[i-1] * i;
Factt[N-1] = _I(Fact[N-1]); DWN(i, N, 1) Factt[i-1] = Factt[i] * i;
*/
/*
int Binom[N][N];
REP(i, N){Binom[i][0] = 1; REP_1(j, i) Binom[i][j] = Binom[i-1][j-1] + Binom[i-1][j];}
*/
/*
const int PMAX = 1;
VI P; bitset<PMAX> isP;
void sieve(){
FOR(i, 2, PMAX){
if (!isP[i]) P.PB(i);
for (int j=0;j<SZ(P)&&i*P[j]<PMAX;++j){
isP[i*P[j]]=1; if (!(i%P[j])) break;
}
}
}
*/
/*
inline int phi(int n){
int res = n; for (int i=2;sqr(i)<=n;++i) if (!(n%i)){
DEC(res, qtt(res, i));
do{n /= i;} while(!(n%i));
}
if (n != 1)
DEC(res, qtt(res, n));
return res;
}
*/
/*LL d, x, y; void exGcd(LL a, LL b){
if(!b) x = 1, y = 0, d = a;
else{
exGcd(b, a%b); LL t = y;
y = x - (a/b)*y, x = t;
}
}*/
} using namespace NT;//}
// <<= '9. Comutational Geometry .,//{
namespace CG{
#define cPo const Po&
#define cLine const Line&
#define cSeg const Seg&
inline DB dist2(DB x,DB y){return sqr(x)+sqr(y);}
struct Po{
DB x,y;Po(DB x=0,DB y=0):x(x),y(y){}
void in(){RF(x,y);}void out(){printf("(%.2f,%.2f)",x,y);}
inline friend istream&operator>>(istream&i,Po&p){return i>>p.x>>p.y;}
inline friend ostream&operator<<(ostream&o,Po p){return o<<"("<<p.x<<", "<<p.y<< ")";}
Po operator-()const{return Po(-x,-y);}
Po&operator+=(cPo p){x+=p.x,y+=p.y;rTs;}Po&operator-=(cPo p){x-=p.x,y-=p.y;rTs;}
Po&operator*=(DB k){x*=k,y*=k;rTs;}Po&operator/=(DB k){x/=k,y/=k;rTs;}
Po&operator*=(cPo p){rTs=Ts*p;}Po&operator/=(cPo p){rTs=Ts/p;}
Po operator+(cPo p)const{return Po(x+p.x,y+p.y);}Po operator-(cPo p)const{return Po(x-p.x,y-p.y);}
Po operator*(DB k)const{return Po(x*k,y*k);}Po operator/(DB k)const{return Po(x/k,y/k);}
Po operator*(cPo p)const{return Po(x*p.x-y*p.y,y*p.x+x*p.y);}Po operator/(cPo p)const{return Po(x*p.x+y*p.y,y*p.x-x*p.y)/p.len2();}
bool operator==(cPo p)const{return!sgn(x,p.x)&&!sgn(y,p.y);};bool operator!=(cPo p)const{return sgn(x,p.x)||sgn(y,p.y);}
bool operator<(cPo p)const{return sgn(x,p.x)<0||!sgn(x,p.x)&&sgn(y,p.y)<0;}bool operator<=(cPo p)const{return sgn(x,p.x)<0||!sgn(x,p.x)&&sgn(y,p.y)<=0;}
bool operator>(cPo p)const{return!(Ts<=p);}bool operator >=(cPo p)const{return!(Ts<p);}
DB len2()const{return dist2(x,y);}DB len()const{return sqrt(len2());}DB arg()const{return atan2(y,x);}
Po&_1(){rTs/=len();}Po&conj(){y=-y;rTs;}Po&lt(){swap(x,y),x=-x;rTs;}Po&rt(){swap(x,y),y=-y;rTs;}
Po&rot(DB a,cPo o=Po()){Ts-=o;Ts*=Po(cos(a),sin(a));rTs+=o;}
};
inline DB dot(DB x1,DB y1,DB x2,DB y2){return x1*x2+y1*y2;}
inline DB dot(cPo a,cPo b){return dot(a.x,a.y,b.x,b.y);}
inline DB dot(cPo p0,cPo p1,cPo p2){return dot(p1-p0,p2-p0);}
inline DB det(DB x1,DB y1,DB x2,DB y2){return x1*y2-x2*y1;}
inline DB det(cPo a,cPo b){return det(a.x,a.y,b.x,b.y);}
inline DB det(cPo p0,cPo p1,cPo p2){return det(p1-p0,p2-p0);}
inline DB ang(cPo p0,cPo p1){return acos(dot(p0,p1)/p0.len()/p1.len());}
inline DB ang(cPo p0,cPo p1,cPo p2){return ang(p1-p0,p2-p0);}
inline DB ang(cPo p0,cPo p1,cPo p2,cPo p3){return ang(p1-p0,p3-p2);}
inline DB dist2(const Po &a, const Po &b){return dist2(a.x-b.x, a.y-b.y);}
template<class T1, class T2> inline int dett(const T1 &x, const T2 &y){return sgn(det(x, y));}
template<class T1, class T2, class T3> inline int dett(const T1 &x, const T2 &y, const T3 &z){return sgn(det(x, y, z));}
template<class T1, class T2, class T3, class T4> inline int dett(const T1 &x, const T2 &y, const T3 &z, const T4 &w){return sgn(det(x, y, z, w));}
template<class T1, class T2> inline int dott(const T1 &x, const T2 &y){return sgn(dot(x, y));}
template<class T1, class T2, class T3> inline int dott(const T1 &x, const T2 &y, const T3 &z){return sgn(dot(x, y, z));}
template<class T1, class T2, class T3, class T4> inline int dott(const T1 &x, const T2 &y, const T3 &z, const T4 &w){return sgn(dot(x, y, z, w));}
template<class T1, class T2> inline DB arg(const T1 &x, const T2 &y){DB a=ang(x,y);return~dett(x,y)?a:2*PI-a;}
template<class T1, class T2, class T3> inline DB arg(const T1 &x, const T2 &y, const T3 &z){DB a=ang(x,y,z);return~dett(x,y,z)?a:2*PI-a;}
template<class T1, class T2, class T3, class T4> inline DB arg(const T1 &x, const T2 &y, const T3 &z, const T4 &w){DB a=ang(x,y,z,w);return~dett(x,y,z,w)?a:2*PI-a;}
template<class T1, class T2> inline DB dist(const T1 &x, const T2 &y){return sqrt(dist2(x, y));}
template<class T1, class T2, class T3> inline DB dist(const T1 &x, const T2 &y, const T3 &z){return sqrt(dist2(x, y, z));}
inline Po _1(Po p){return p._1();}inline Po conj(Po p){return p.conj();}
inline Po lt(Po p){return p.lt();}inline Po rt(Po p){return p.rt();}
inline Po rot(Po p,DB a,cPo o=Po()){return p.rot(a,o);}
inline Po operator *(DB k,cPo p){return p*k;}
inline Po operator /(DB k,cPo p){return conj(p)*k/p.len2();}
typedef vector<Po> VP;
struct Line{
Po a,b;Line(cPo a=Po(),cPo b=Po()):a(a),b(b){}
Line(DB x0,DB y0,DB x1,DB y1):a(Po(x0,y0)),b(Po(x1,y1)){}
Line(cLine l):a(l.a),b(l.b){}
//Ax+By+C=0
Line(DB A,DB B,DB C){
C=-C;if(!::sgn(A))a=Po(0,C/B),b=Po(1,C/B);
else if(!::sgn(B))a=Po(C/A,0),b=Po(C/A,1);
else a=Po(0,C/B),b=Po(1,(C-A)/B);
}
void in(){a.in(),b.in();}
inline friend istream&operator>>(istream&i,Line& p){return i>>p.a>>p.b;}
inline friend ostream&operator<<(ostream&o,Line p){return o<<p.a<<"-"<< p.b;}
Line operator+(cPo x)const{return Line(a+x,b+x);}
Line operator-(cPo x)const{return Line(a-x,b-x);}
Line operator*(DB k)const{return Line(a*k,b*k);}
Line operator/(DB k)const{return Line(a/k,b/k);}
Po operator*(cLine)const;
Po d()const{return b-a;}DB len2()const{return d().len2();}DB len()const{return d().len();}DB arg()const{return d().arg();}
int sgn(cPo p)const{return dett(a, b, p);}
int sgn(cLine)const;
bool sameSgn(cPo p1,cPo p2)const{return sgn(p1)==sgn(p2);}
void getEquation(DB&K,DB&B)const{
K = ::sgn(a.x, b.x) ? (b.y-a.y)/(b.x-a.x) : OO;
B = a.y - K*a.x;
}
void getEquation(DB&A,DB&B,DB&C)const{A=a.y-b.y,B=b.x-a.x,C=det(a, b);}
Line&push(DB r){ // 正数右手螺旋向里
Po v=d()._1().lt()*r;a+=v,b+=v; rTs;
}
};
inline DB dot(cLine l1,cLine l2){return dot(l1.d(),l2.d());}
inline DB dot(cLine l,cPo p){return dot(l.a,l.b,p);}
inline DB dot(cPo p,cLine l){return dot(p,l.a,l.b);}
inline DB det(cLine l1,cLine l2){return det(l1.d(),l2.d());}
inline DB det(cLine l,cPo p){return det(l.a,l.b,p);}
inline DB det(cPo p,cLine l){return det(p,l.a,l.b);}
inline DB ang(cLine l0,cLine l1){return ang(l0.d(),l1.d());}
inline DB ang(cLine l,cPo p){return ang(l.a,l.b,p);}
inline DB ang(cPo p,cLine l){return ang(p,l.a,l.b);}
inline int Line::sgn(cLine l)const{return dett(Ts, l);}
inline Po Line::operator*(cLine l)const{return a+d()*det(a,l)/det(Ts,l);}
inline Po operator&(cPo p,cLine l){return l*Line(p,p+l.d().lt());}
inline Po operator%(cPo p,cLine l){return p&l*2-p;}
inline Line push(Line l, DB r){return l.push(r);}
struct Seg: public Line{
Seg(cPo a=Po(),cPo b=Po()):Line(a,b){}
Seg(DB x0,DB y0,DB x1,DB y1):Line(x0,y0,x1,y1){}
Seg(cLine l):Line(l){}
Seg(const Po &a,DB alpha):Line(a,alpha){}
Seg(DB A,DB B,DB C):Line(A,B,C){}
inline int sgn(cPo p)const;
inline int sgn(cLine l)const;
inline bool qrt(cSeg l)const;
inline int sgn(cSeg l)const;
};
// -1不相交 0相交（不规范） 1相交（规范）
inline int Seg::sgn(cPo p)const{return -dott(p,a,b);}
inline int Seg::sgn(cLine l)const{return sgn(Ts*l);}
// quick_rejection_test
inline bool Seg::qrt(cSeg l)const{
return min(a.x,b.x)<=max(l.a.x,l.b.x)&&min(l.a.x,l.b.x)<=max(a.x,b.x)&&
min(a.y,b.y)<=max(l.a.y,l.b.y)&&min(l.a.y,l.b.y)<=max(a.y,b.y);
}
inline int Seg::sgn(cSeg l)const{
if (!qrt(l)) return -1;
/*return
(dett(a,b,l.a)*dett(a,b,l.b)<=0 &&
dett(l.a,l.b,a)*dett(l.a,l.b,b)<=0)?1:-1;*/
int d1=dett(a,b,l.a),d2=dett(a,b,l.b),d3=dett(l.a,l.b,a),d4=dett(l.a,l.b,b);
if ((d1^d2)==-2&&(d3^d4)==-2)return 1;
return ((!d1&&dott(l.a-a,l.a-b)<=0)||(!d2&&dott(l.b-a,l.b-b)<=0)||
(!d3&&dott(a-l.a,a-l.b)<=0)||(!d4&&dott(b-l.a,b-l.b)<=0))?0:-1;
}
//inline DB dist2(cLine l,cPo p){return sqr(fabs(dot(lt(l.d()), p-l.a)))/l.len2();}
inline DB dist2(cLine l,cPo p){return sqr(fabs(det(l.d(), p-l.a)))/l.len2();}
inline DB dist2(cLine l1,cLine l2){return dett(l1,l2)?0:dist2(l1,l2.a);}
inline DB dist2(cSeg l,cPo p){
Po pa = p - l.a, pb = p - l.b;
if (dott(l.d(), pa) <= 0) return pa.len2();
if (dott(l.d(), pb) >= 0) return pb.len2();
return dist2(Line(l), p);
}
inline DB dist2(cSeg s,cLine l){
Po v1=s.a-l.a,v2=s.b-l.a;DB d1=det(l.d(),v1),d2=det(l.d(),v2);
return sgn(d1)!=sgn(d2) ? 0 : sqr(min(fabs(d1), fabs(d2)))/l.len2();
}
inline DB dist2(cSeg l1,cSeg l2){
if (~l1.sgn(l2)) return 0;
else return min(dist2(l2,l1.a), dist2(l2,l1.b), dist2(l1,l2.a), dist2(l1,l2.b));
}
template<class T1, class T2> inline DB dist2(const T1& a, const T2& b){
return dist2(b, a);
}
Po getPo(){Po p;p.in();return p;}
Line getLine(){Line l;l.in();return l;}
DB getArea(const VP& P){DB z=0;FOR(i,1,SZ(P))z+=det(P[i-1],P[i]);return z;}
DB getPeri(const VP& P){DB z=0;FOR(i,1,SZ(P))z+=dist(P[i-1],P[i]);return z;}
} using namespace CG;//}
//}
/** I/O Accelerator Interface .. **/ //{
#define g (c=getchar())
#define d isdigit(g)
#define p x=x*10+c-'0'
#define n x=x*10+'0'-c
#define pp l/=10,p
#define nn l/=10,n
template<class T> inline T& RD(T &x){
char c;while(!d);x=c-'0';while(d)p;
return x;
}
template<class T> inline T& RDD(T &x){
char c;while(g,c!='-'&&!isdigit(c));
if (c=='-'){x='0'-g;while(d)n;}
else{x=c-'0';while(d)p;}
return x;
}
inline DB& RF(DB &x){
//scanf("%lf", &x);
char c;while(g,c!='-'&&c!='.'&&!isdigit(c));
if(c=='-')if(g=='.'){x=0;DB l=1;while(d)nn;x*=l;}
else{x='0'-c;while(d)n;if(c=='.'){DB l=1;while(d)nn;x*=l;}}
else if(c=='.'){x=0;DB l=1;while(d)pp;x*=l;}
else{x=c-'0';while(d)p;if(c=='.'){DB l=1;while(d)pp;x*=l;}}
return x;
}
#undef nn
#undef pp
#undef n
#undef p
#undef d
#undef g
inline char* RS(char *s){
//gets(s);
scanf("%s", s);
return s;
}
LL last_ans; int Case; template<class T> inline void OT(const T &x){
//printf("Case #%d: ", ++Case);
//printf("%lld\n", x);
printf("%.3f\n", x);
//printf("%d\n", x);
//cout << x << endl;
//last_ans = x;
}
//}
//}/* .................................................................................................................................. */
const int N = int(2e5) + 9;
int x[N], y[N], n; DB slope[N];
int D;
inline DB yy(int i, DB xx){
return y[i] + (xx-x[i])*slope[i];
}
inline DB s(int i, DB st, DB ed){
return (ed-st)*(yy(i,st)+yy(i,ed));
}
int main(){
#ifndef ONLINE_JUDGE
freopen("in.txt", "r", stdin);
//freopen("out.txt", "w", stdout);
#endif
Rush{
RD(n); RD(); REP(i, n) RD(x[i], y[i]); RD(D)*=2;
REP(i, n-1) slope[i] = (DB)(y[i+1]-y[i])/(x[i+1]-x[i]);
DB res = 0, pre = 0; int r; REP_N(r, n-1){
if (x[r+1] >= D) break;
pre += s(r,x[r],x[r+1]);
}
checkMax(res, pre += s(r, x[r], D));
int l=0,ll=0,rr=D;r+=rr==x[r+1];
for (;r<n-1;l+=ll==x[l+1],r+=rr==x[r+1]){
int d = min(x[r+1]-rr, x[l+1]-ll); DB a = slope[r]-slope[l], b = (yy(r,rr)-yy(l,ll))*2; if (sgn(a)){
DB dd = -b/(2*a); if (sgn(.0, dd) < 0 && sgn(dd, DB(d)) < 0){
checkMax(res, pre-(b*b/a/4));
}
}
checkMax(res, pre += s(r,rr,rr+d)-s(l,ll,ll+d));
ll+=d,rr+=d;
}
OT(res/D/2);
}
}
Raw
I.cpp
/** Micro Mezz Macro Flation -- Overheated Economy ., Last Update: May. 7th 2014 **/ //{
/** Header .. **/ //{
#pragma comment(linker, "/STACK:36777216")
//#pragma GCC optimize ("O2")
#define LOCAL
//#include "testlib.h"
#include <functional>
#include <algorithm>
#include <iostream>
#include <fstream>
#include <sstream>
#include <iomanip>
#include <numeric>
#include <cstring>
#include <climits>
#include <cassert>
#include <complex>
#include <cstdio>
#include <string>
#include <vector>
#include <bitset>
#include <queue>
#include <stack>
#include <cmath>
#include <ctime>
#include <list>
#include <set>
#include <map>
//#include <tr1/unordered_set>
//#include <tr1/unordered_map>
//#include <array>
using namespace std;
#define REP(i, n) for (int i=0;i<n;++i)
#define FOR(i, a, b) for (int i=a;i<b;++i)
#define DWN(i, b, a) for (int i=b-1;i>=a;--i)
#define REP_1(i, n) for (int i=1;i<=n;++i)
#define FOR_1(i, a, b) for (int i=a;i<=b;++i)
#define DWN_1(i, b, a) for (int i=b;i>=a;--i)
#define REP_C(i, n) for (int n____=n,i=0;i<n____;++i)
#define FOR_C(i, a, b) for (int b____=b,i=a;i<b____;++i)
#define DWN_C(i, b, a) for (int a____=a,i=b-1;i>=a____;--i)
#define REP_N(i, n) for (i=0;i<n;++i)
#define FOR_N(i, a, b) for (i=a;i<b;++i)
#define DWN_N(i, b, a) for (i=b-1;i>=a;--i)
#define REP_1_C(i, n) for (int n____=n,i=1;i<=n____;++i)
#define FOR_1_C(i, a, b) for (int b____=b,i=a;i<=b____;++i)
#define DWN_1_C(i, b, a) for (int a____=a,i=b;i>=a____;--i)
#define REP_1_N(i, n) for (i=1;i<=n;++i)
#define FOR_1_N(i, a, b) for (i=a;i<=b;++i)
#define DWN_1_N(i, b, a) for (i=b;i>=a;--i)
#define REP_C_N(i, n) for (int n____=(i=0,n);i<n____;++i)
#define FOR_C_N(i, a, b) for (int b____=(i=0,b);i<b____;++i)
#define DWN_C_N(i, b, a) for (int a____=(i=b-1,a);i>=a____;--i)
#define REP_1_C_N(i, n) for (int n____=(i=1,n);i<=n____;++i)
#define FOR_1_C_N(i, a, b) for (int b____=(i=a,b);i<=b____;++i)
#define DWN_1_C_N(i, b, a) for (int a____=(i=b,a);i>=a____;--i)
#define ECH(it, A) for (__typeof(A.begin()) it=A.begin(); it != A.end(); ++it)
#define REP_S(i, str) for (char*i=str;*i;++i)
#define REP_L(i, hd, suc) for (int i=hd;i;i=suc[i])
#define REP_G(i, u) REP_L(i,hd[u],suc)
#define REP_SS(x, s) for (int x=s;x;x=(x-1)&s)
#define DO(n) for ( int ____n = n; ____n-->0; )
#define REP_2(i, j, n, m) REP(i, n) REP(j, m)
#define REP_2_1(i, j, n, m) REP_1(i, n) REP_1(j, m)
#define REP_3(i, j, k, n, m, l) REP(i, n) REP(j, m) REP(k, l)
#define REP_3_1(i, j, k, n, m, l) REP_1(i, n) REP_1(j, m) REP_1(k, l)
#define REP_4(i, j, k, ii, n, m, l, nn) REP(i, n) REP(j, m) REP(k, l) REP(ii, nn)
#define REP_4_1(i, j, k, ii, n, m, l, nn) REP_1(i, n) REP_1(j, m) REP_1(k, l) REP_1(ii, nn)
#define ALL(A) A.begin(), A.end()
#define LLA(A) A.rbegin(), A.rend()
#define CPY(A, B) memcpy(A, B, sizeof(A))
#define INS(A, P, B) A.insert(A.begin() + P, B)
#define ERS(A, P) A.erase(A.begin() + P)
#define LBD(A, x) (lower_bound(ALL(A), x) - A.begin())
#define UBD(A, x) (lower_bound(ALL(A), x) - A.begin())
#define CTN(T, x) (T.find(x) != T.end())
#define SZ(A) int((A).size())
#define PB push_back
#define MP(A, B) make_pair(A, B)
#define PTT pair<T, T>
#define Ts *this
#define rTs return Ts
#define fi first
#define se second
#define re real()
#define im imag()
#define Rush for(int ____T=RD(); ____T--;)
#define Display(A, n, m) { \
REP(i, n){ \
REP(j, m-1) cout << A[i][j] << " "; \
cout << A[i][m-1] << endl; \
} \
}
#define Display_1(A, n, m) { \
REP_1(i, n){ \
REP_1(j, m-1) cout << A[i][j] << " "; \
cout << A[i][m] << endl; \
} \
}
typedef long long LL;
//typedef long double DB;
typedef double DB;
typedef unsigned uint;
typedef unsigned long long uLL;
typedef vector<int> VI;
typedef vector<char> VC;
typedef vector<string> VS;
typedef vector<LL> VL;
typedef vector<DB> VF;
typedef set<int> SI;
typedef set<string> SS;
typedef map<int, int> MII;
typedef map<string, int> MSI;
typedef pair<int, int> PII;
typedef pair<LL, LL> PLL;
typedef vector<PII> VII;
typedef vector<VI> VVI;
typedef vector<VII> VVII;
template<class T> inline T& RD(T &);
template<class T> inline void OT(const T &);
//inline int RD(){int x; return RD(x);}
inline LL RD(){LL x; return RD(x);}
inline DB& RF(DB &);
inline DB RF(){DB x; return RF(x);}
inline char* RS(char *s);
inline char& RC(char &c);
inline char RC();
inline char& RC(char &c){scanf(" %c", &c); return c;}
inline char RC(){char c; return RC(c);}
//inline char& RC(char &c){c = getchar(); return c;}
//inline char RC(){return getchar();}
template<class T> inline T& RDD(T &);
inline LL RDD(){LL x; return RDD(x);}
template<class T0, class T1> inline T0& RD(T0 &x0, T1 &x1){RD(x0), RD(x1); return x0;}
template<class T0, class T1, class T2> inline T0& RD(T0 &x0, T1 &x1, T2 &x2){RD(x0), RD(x1), RD(x2); return x0;}
template<class T0, class T1, class T2, class T3> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3){RD(x0), RD(x1), RD(x2), RD(x3); return x0;}
template<class T0, class T1, class T2, class T3, class T4> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4); return x0;}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5); return x0;}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5, T6 &x6){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5), RD(x6); return x0;}
template<class T0, class T1> inline void OT(const T0 &x0, const T1 &x1){OT(x0), OT(x1);}
template<class T0, class T1, class T2> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2){OT(x0), OT(x1), OT(x2);}
template<class T0, class T1, class T2, class T3> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3){OT(x0), OT(x1), OT(x2), OT(x3);}
template<class T0, class T1, class T2, class T3, class T4> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3, const T4 &x4){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3, const T4 &x4, const T5 &x5){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3, const T4 &x4, const T5 &x5, const T6 &x6){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5), OT(x6);}
inline char& RC(char &a, char &b){RC(a), RC(b); return a;}
inline char& RC(char &a, char &b, char &c){RC(a), RC(b), RC(c); return a;}
inline char& RC(char &a, char &b, char &c, char &d){RC(a), RC(b), RC(c), RC(d); return a;}
inline char& RC(char &a, char &b, char &c, char &d, char &e){RC(a), RC(b), RC(c), RC(d), RC(e); return a;}
inline char& RC(char &a, char &b, char &c, char &d, char &e, char &f){RC(a), RC(b), RC(c), RC(d), RC(e), RC(f); return a;}
inline char& RC(char &a, char &b, char &c, char &d, char &e, char &f, char &g){RC(a), RC(b), RC(c), RC(d), RC(e), RC(f), RC(g); return a;}
inline DB& RF(DB &a, DB &b){RF(a), RF(b); return a;}
inline DB& RF(DB &a, DB &b, DB &c){RF(a), RF(b), RF(c); return a;}
inline DB& RF(DB &a, DB &b, DB &c, DB &d){RF(a), RF(b), RF(c), RF(d); return a;}
inline DB& RF(DB &a, DB &b, DB &c, DB &d, DB &e){RF(a), RF(b), RF(c), RF(d), RF(e); return a;}
inline DB& RF(DB &a, DB &b, DB &c, DB &d, DB &e, DB &f){RF(a), RF(b), RF(c), RF(d), RF(e), RF(f); return a;}
inline DB& RF(DB &a, DB &b, DB &c, DB &d, DB &e, DB &f, DB &g){RF(a), RF(b), RF(c), RF(d), RF(e), RF(f), RF(g); return a;}
inline void RS(char *s1, char *s2){RS(s1), RS(s2);}
inline void RS(char *s1, char *s2, char *s3){RS(s1), RS(s2), RS(s3);}
template<class T0,class T1>inline void RDD(T0&a, T1&b){RDD(a),RDD(b);}
template<class T0,class T1,class T2>inline void RDD(T0&a, T1&b, T2&c){RDD(a),RDD(b),RDD(c);}
template<class T> inline void RST(T &A){memset(A, 0, sizeof(A));}
template<class T> inline void FLC(T &A, int x){memset(A, x, sizeof(A));}
template<class T> inline void CLR(T &A){A.clear();}
template<class T0, class T1> inline void RST(T0 &A0, T1 &A1){RST(A0), RST(A1);}
template<class T0, class T1, class T2> inline void RST(T0 &A0, T1 &A1, T2 &A2){RST(A0), RST(A1), RST(A2);}
template<class T0, class T1, class T2, class T3> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3){RST(A0), RST(A1), RST(A2), RST(A3);}
template<class T0, class T1, class T2, class T3, class T4> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5), RST(A6);}
template<class T0, class T1> inline void FLC(T0 &A0, T1 &A1, int x){FLC(A0, x), FLC(A1, x);}
template<class T0, class T1, class T2> inline void FLC(T0 &A0, T1 &A1, T2 &A2, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x);}
template<class T0, class T1, class T2, class T3> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x);}
template<class T0, class T1, class T2, class T3, class T4> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x), FLC(A5, x);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x), FLC(A5, x), FLC(A6, x);}
template<class T> inline void CLR(priority_queue<T, vector<T>, less<T> > &Q){while (!Q.empty()) Q.pop();}
template<class T> inline void CLR(priority_queue<T, vector<T>, greater<T> > &Q){while (!Q.empty()) Q.pop();}
template<class T> inline void CLR(stack<T> &S){while (!S.empty()) S.pop();}
template<class T0, class T1> inline void CLR(T0 &A0, T1 &A1){CLR(A0), CLR(A1);}
template<class T0, class T1, class T2> inline void CLR(T0 &A0, T1 &A1, T2 &A2){CLR(A0), CLR(A1), CLR(A2);}
template<class T0, class T1, class T2, class T3> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3){CLR(A0), CLR(A1), CLR(A2), CLR(A3);}
template<class T0, class T1, class T2, class T3, class T4> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5), CLR(A6);}
template<class T> inline void CLR(T &A, int n){REP(i, n) CLR(A[i]);}
template<class T> inline bool EPT(T &a){return a.empty();}
template<class T> inline T& SRT(T &A){sort(ALL(A)); return A;}
template<class T, class C> inline T& SRT(T &A, C B){sort(ALL(A), B); return A;}
template<class T> inline T& RVS(T &A){reverse(ALL(A)); return A;}
template<class T> inline T& UNQQ(T &A){A.resize(unique(ALL(A))-A.begin());return A;}
template<class T> inline T& UNQ(T &A){SRT(A);return UNQQ(A);}
//}
/** Constant List .. **/ //{
const int MOD = int(1e9) + 7;
const int INF = 0x3f3f3f3f;
const LL INFF = 0x3f3f3f3f3f3f3f3fLL;
const DB EPS = 1e-9;
const DB OO = 1e20;
const DB PI = acos(-1.0); //M_PI;
const int dx[] = {-1, 0, 1, 0};
const int dy[] = {0, 1, 0, -1};
//}
/** Add On .. **/ //{
// <<= '0. Nichi Joo ., //{
template<class T> inline T& checkMin(T &a,const T b){if (b<a) a=b;return a;}
template<class T> inline T& checkMax(T &a,const T b){if (a<b) a=b;return a;}
template<class T> inline T& checkMin(T &a, T &b, const T x){checkMin(a, x), checkMin(b, x);return a;}
template<class T> inline T& checkMax(T &a, T &b, const T x){checkMax(a, x), checkMax(b, x);return a;}
template <class T, class C> inline T& checkMin(T& a, const T b, C c){if (c(b,a)) a = b;return a;}
template <class T, class C> inline T& checkMax(T& a, const T b, C c){if (c(a,b)) a = b;return a;}
template<class T> inline T min(T a, T b, T c){return min(min(a, b), c);}
template<class T> inline T max(T a, T b, T c){return max(max(a, b), c);}
template<class T> inline T min(T a, T b, T c, T d){return min(min(a, b), min(c, d));}
template<class T> inline T max(T a, T b, T c, T d){return max(max(a, b), max(c, d));}
template<class T> inline T min(T a, T b, T c, T d, T e){return min(min(min(a,b),min(c,d)),e);}
template<class T> inline T max(T a, T b, T c, T d, T e){return max(max(max(a,b),max(c,d)),e);}
template<class T> inline T sqr(T a){return a*a;}
template<class T> inline T cub(T a){return a*a*a;}
template<class T> inline T ceil(T x, T y){return (x - 1) / y + 1;}
template<class T> T abs(T x){return x>0?x:-x;}
inline int sgn(DB x){return x < -EPS ? -1 : x > EPS;}
inline int sgn(DB x, DB y){return sgn(x - y);}
inline DB cos(DB a, DB b, DB c){return (sqr(a)+sqr(b)-sqr(c))/(2*a*b);}
inline DB cot(DB x){return 1./tan(x);};
inline DB sec(DB x){return 1./cos(x);};
inline DB csc(DB x){return 1./sin(x);};
//}
// <<= '1. Bitwise Operation ., //{
namespace BO{
inline bool _1(int x, int i){return bool(x&1<<i);}
inline bool _1(LL x, int i){return bool(x&1LL<<i);}
inline LL _1(int i){return 1LL<<i;}
inline LL _U(int i){return _1(i) - 1;};
inline int reverse_bits(int x){
x = ((x >> 1) & 0x55555555) | ((x << 1) & 0xaaaaaaaa);
x = ((x >> 2) & 0x33333333) | ((x << 2) & 0xcccccccc);
x = ((x >> 4) & 0x0f0f0f0f) | ((x << 4) & 0xf0f0f0f0);
x = ((x >> 8) & 0x00ff00ff) | ((x << 8) & 0xff00ff00);
x = ((x >>16) & 0x0000ffff) | ((x <<16) & 0xffff0000);
return x;
}
inline LL reverse_bits(LL x){
x = ((x >> 1) & 0x5555555555555555LL) | ((x << 1) & 0xaaaaaaaaaaaaaaaaLL);
x = ((x >> 2) & 0x3333333333333333LL) | ((x << 2) & 0xccccccccccccccccLL);
x = ((x >> 4) & 0x0f0f0f0f0f0f0f0fLL) | ((x << 4) & 0xf0f0f0f0f0f0f0f0LL);
x = ((x >> 8) & 0x00ff00ff00ff00ffLL) | ((x << 8) & 0xff00ff00ff00ff00LL);
x = ((x >>16) & 0x0000ffff0000ffffLL) | ((x <<16) & 0xffff0000ffff0000LL);
x = ((x >>32) & 0x00000000ffffffffLL) | ((x <<32) & 0xffffffff00000000LL);
return x;
}
template<class T> inline bool odd(T x){return x&1;}
template<class T> inline bool even(T x){return !odd(x);}
template<class T> inline T low_bit(T x) {return x & -x;}
template<class T> inline T high_bit(T x) {T p = low_bit(x);while (p != x) x -= p, p = low_bit(x);return p;}
template<class T> inline T cover_bit(T x){T p = 1; while (p < x) p <<= 1;return p;}
template<class T> inline int cover_idx(T x){int p = 0; while (_1(p) < x ) ++p; return p;}
inline int clz(int x){return __builtin_clz(x);}
inline int clz(LL x){return __builtin_clzll(x);}
inline int ctz(int x){return __builtin_ctz(x);}
inline int ctz(LL x){return __builtin_ctzll(x);}
inline int lg2(int x){return !x ? -1 : 31 - clz(x);}
inline int lg2(LL x){return !x ? -1 : 63 - clz(x);}
inline int low_idx(int x){return !x ? -1 : ctz(x);}
inline int low_idx(LL x){return !x ? -1 : ctz(x);}
inline int high_idx(int x){return lg2(x);}
inline int high_idx(LL x){return lg2(x);}
inline int parity(int x){return __builtin_parity(x);}
inline int parity(LL x){return __builtin_parityll(x);}
inline int count_bits(int x){return __builtin_popcount(x);}
inline int count_bits(LL x){return __builtin_popcountll(x);}
} using namespace BO;//}
// <<= '2. Number Theory .,//{
namespace NT{
inline LL gcd(LL a, LL b){return __gcd(a, b);}
inline LL lcm(LL a, LL b){return a*b/gcd(a,b);}
inline void INC(int &a, int b){a += b; if (a >= MOD) a -= MOD;}
inline int sum(int a, int b){a += b; if (a >= MOD) a -= MOD; return a;}
inline void DEC(int &a, int b){a -= b; if (a < 0) a += MOD;}
inline int dff(int a, int b){a -= b; if (a < 0) a += MOD; return a;}
inline void MUL(int &a, int b){a = (LL)a * b % MOD;}
inline int pdt(int a, int b){return (LL)a * b % MOD;}
inline int gcd(int m, int n, int &x, int &y){
x = 1, y = 0; int xx = 0, yy = 1, q;
while (1){
q = m / n, m %= n;
if (!m){x = xx, y = yy; return n;}
DEC(x, pdt(q, xx)), DEC(y, pdt(q, yy));
q = n / m, n %= m;
if (!n) return m;
DEC(xx, pdt(q, x)), DEC(yy, pdt(q, y));
}
}
inline int sum(int a, int b, int c){return sum(a, sum(b, c));}
inline int sum(int a, int b, int c, int d){return sum(sum(a, b), sum(c, d));}
inline int pdt(int a, int b, int c){return pdt(a, pdt(b, c));}
inline int pdt(int a, int b, int c, int d){return pdt(pdt(a, b), pdt(c, d));}
inline int pow(int a, LL b){
int c(1); while (b){
if (b&1) MUL(c, a);
MUL(a, a), b >>= 1;
}
return c;
}
template<class T> inline T pow(T a, LL b){
T c(1); while (b){
if (b&1) c *= a;
a *= a, b >>= 1;
}
return c;
}
template<class T> inline T pow(T a, int b){
return pow(a, (LL)b);
}
inline int _I(int b){
int a = MOD, x1 = 0, x2 = 1, q;
while (true){
q = a / b, a %= b;
if (!a) return (x2 + MOD) % MOD;
DEC(x1, pdt(q, x2));
q = b / a, b %= a;
if (!b) return (x1 + MOD) % MOD;
DEC(x2, pdt(q, x1));
}
}
inline void DIV(int &a, int b){MUL(a, _I(b));}
inline int qtt(int a, int b){return pdt(a, _I(b));}
struct Int{
int val;
operator int() const{return val;}
Int(int val = 0):val(val){
val %= MOD; if (val < 0) val += MOD;
}
Int(LL _val){
_val %= MOD; if (_val < 0) _val += MOD;
val = _val;
}
Int& operator +=(const int& rhs){
INC(val, rhs);
return *this;
}
Int operator +(const int& rhs) const{
return sum(val, rhs);
}
Int& operator -=(const int& rhs){
DEC(val, rhs);
return *this;
}
Int operator -(const int& rhs) const{
return dff(val, rhs);
}
Int& operator *=(const int& rhs){
MUL(val, rhs);
return *this;
}
Int operator *(const int& rhs) const{
return pdt(val, rhs);
}
Int& operator /=(const int& rhs){
DIV(val, rhs);
return *this;
}
Int operator /(const int& rhs) const{
return qtt(val, rhs);
}
Int operator-()const{
return MOD-*this;
}
};
/*
Int Fact[N], Factt[N]; Int Binom(int n, int m){
return Fact[n] * Factt[m] * Factt[n-m];
}
*/
/*
Fact[0] = 1; REP_1(i, N-1) Fact[i] = Fact[i-1] * i;
Factt[N-1] = _I(Fact[N-1]); DWN(i, N, 1) Factt[i-1] = Factt[i] * i;
*/
/*
int Binom[N][N];
REP(i, N){Binom[i][0] = 1; REP_1(j, i) Binom[i][j] = Binom[i-1][j-1] + Binom[i-1][j];}
*/
/*
const int PMAX = 1;
VI P; bitset<PMAX> isP;
void sieve(){
FOR(i, 2, PMAX){
if (!isP[i]) P.PB(i);
for (int j=0;j<SZ(P)&&i*P[j]<PMAX;++j){
isP[i*P[j]]=1; if (!(i%P[j])) break;
}
}
}
*/
/*
inline int phi(int n){
int res = n; for (int i=2;sqr(i)<=n;++i) if (!(n%i)){
DEC(res, qtt(res, i));
do{n /= i;} while(!(n%i));
}
if (n != 1)
DEC(res, qtt(res, n));
return res;
}
*/
/*LL d, x, y; void exGcd(LL a, LL b){
if(!b) x = 1, y = 0, d = a;
else{
exGcd(b, a%b); LL t = y;
y = x - (a/b)*y, x = t;
}
}*/
} using namespace NT;//}
// <<= '9. Comutational Geometry .,//{
namespace CG{
#define cPo const Po&
#define cLine const Line&
#define cSeg const Seg&
inline DB dist2(DB x,DB y){return sqr(x)+sqr(y);}
struct Po{
DB x,y;Po(DB x=0,DB y=0):x(x),y(y){}
void in(){RF(x,y);}void out(){printf("(%.2f,%.2f)",x,y);}
inline friend istream&operator>>(istream&i,Po&p){return i>>p.x>>p.y;}
inline friend ostream&operator<<(ostream&o,Po p){return o<<"("<<p.x<<", "<<p.y<< ")";}
Po operator-()const{return Po(-x,-y);}
Po&operator+=(cPo p){x+=p.x,y+=p.y;rTs;}Po&operator-=(cPo p){x-=p.x,y-=p.y;rTs;}
Po&operator*=(DB k){x*=k,y*=k;rTs;}Po&operator/=(DB k){x/=k,y/=k;rTs;}
Po&operator*=(cPo p){rTs=Ts*p;}Po&operator/=(cPo p){rTs=Ts/p;}
Po operator+(cPo p)const{return Po(x+p.x,y+p.y);}Po operator-(cPo p)const{return Po(x-p.x,y-p.y);}
Po operator*(DB k)const{return Po(x*k,y*k);}Po operator/(DB k)const{return Po(x/k,y/k);}
Po operator*(cPo p)const{return Po(x*p.x-y*p.y,y*p.x+x*p.y);}Po operator/(cPo p)const{return Po(x*p.x+y*p.y,y*p.x-x*p.y)/p.len2();}
bool operator==(cPo p)const{return!sgn(x,p.x)&&!sgn(y,p.y);};bool operator!=(cPo p)const{return sgn(x,p.x)||sgn(y,p.y);}
bool operator<(cPo p)const{return sgn(x,p.x)<0||!sgn(x,p.x)&&sgn(y,p.y)<0;}bool operator<=(cPo p)const{return sgn(x,p.x)<0||!sgn(x,p.x)&&sgn(y,p.y)<=0;}
bool operator>(cPo p)const{return!(Ts<=p);}bool operator >=(cPo p)const{return!(Ts<p);}
DB len2()const{return dist2(x,y);}DB len()const{return sqrt(len2());}DB arg()const{return atan2(y,x);}
Po&_1(){rTs/=len();}Po&conj(){y=-y;rTs;}Po&lt(){swap(x,y),x=-x;rTs;}Po&rt(){swap(x,y),y=-y;rTs;}
Po&rot(DB a,cPo o=Po()){Ts-=o;Ts*=Po(cos(a),sin(a));rTs+=o;}
};
inline DB dot(DB x1,DB y1,DB x2,DB y2){return x1*x2+y1*y2;}
inline DB dot(cPo a,cPo b){return dot(a.x,a.y,b.x,b.y);}
inline DB dot(cPo p0,cPo p1,cPo p2){return dot(p1-p0,p2-p0);}
inline DB det(DB x1,DB y1,DB x2,DB y2){return x1*y2-x2*y1;}
inline DB det(cPo a,cPo b){return det(a.x,a.y,b.x,b.y);}
inline DB det(cPo p0,cPo p1,cPo p2){return det(p1-p0,p2-p0);}
inline DB ang(cPo p0,cPo p1){return acos(dot(p0,p1)/p0.len()/p1.len());}
inline DB ang(cPo p0,cPo p1,cPo p2){return ang(p1-p0,p2-p0);}
inline DB ang(cPo p0,cPo p1,cPo p2,cPo p3){return ang(p1-p0,p3-p2);}
inline DB dist2(const Po &a, const Po &b){return dist2(a.x-b.x, a.y-b.y);}
template<class T1, class T2> inline int dett(const T1 &x, const T2 &y){return sgn(det(x, y));}
template<class T1, class T2, class T3> inline int dett(const T1 &x, const T2 &y, const T3 &z){return sgn(det(x, y, z));}
template<class T1, class T2, class T3, class T4> inline int dett(const T1 &x, const T2 &y, const T3 &z, const T4 &w){return sgn(det(x, y, z, w));}
template<class T1, class T2> inline int dott(const T1 &x, const T2 &y){return sgn(dot(x, y));}
template<class T1, class T2, class T3> inline int dott(const T1 &x, const T2 &y, const T3 &z){return sgn(dot(x, y, z));}
template<class T1, class T2, class T3, class T4> inline int dott(const T1 &x, const T2 &y, const T3 &z, const T4 &w){return sgn(dot(x, y, z, w));}
template<class T1, class T2> inline DB arg(const T1 &x, const T2 &y){DB a=ang(x,y);return~dett(x,y)?a:2*PI-a;}
template<class T1, class T2, class T3> inline DB arg(const T1 &x, const T2 &y, const T3 &z){DB a=ang(x,y,z);return~dett(x,y,z)?a:2*PI-a;}
template<class T1, class T2, class T3, class T4> inline DB arg(const T1 &x, const T2 &y, const T3 &z, const T4 &w){DB a=ang(x,y,z,w);return~dett(x,y,z,w)?a:2*PI-a;}
template<class T1, class T2> inline DB dist(const T1 &x, const T2 &y){return sqrt(dist2(x, y));}
template<class T1, class T2, class T3> inline DB dist(const T1 &x, const T2 &y, const T3 &z){return sqrt(dist2(x, y, z));}
inline Po _1(Po p){return p._1();}inline Po conj(Po p){return p.conj();}
inline Po lt(Po p){return p.lt();}inline Po rt(Po p){return p.rt();}
inline Po rot(Po p,DB a,cPo o=Po()){return p.rot(a,o);}
inline Po operator *(DB k,cPo p){return p*k;}
inline Po operator /(DB k,cPo p){return conj(p)*k/p.len2();}
typedef vector<Po> VP;
struct Line{
Po a,b;Line(cPo a=Po(),cPo b=Po()):a(a),b(b){}
Line(DB x0,DB y0,DB x1,DB y1):a(Po(x0,y0)),b(Po(x1,y1)){}
Line(cLine l):a(l.a),b(l.b){}
//Ax+By+C=0
Line(DB A,DB B,DB C){
C=-C;if(!::sgn(A))a=Po(0,C/B),b=Po(1,C/B);
else if(!::sgn(B))a=Po(C/A,0),b=Po(C/A,1);
else a=Po(0,C/B),b=Po(1,(C-A)/B);
}
void in(){a.in(),b.in();}
inline friend istream&operator>>(istream&i,Line& p){return i>>p.a>>p.b;}
inline friend ostream&operator<<(ostream&o,Line p){return o<<p.a<<"-"<< p.b;}
Line operator+(cPo x)const{return Line(a+x,b+x);}
Line operator-(cPo x)const{return Line(a-x,b-x);}
Line operator*(DB k)const{return Line(a*k,b*k);}
Line operator/(DB k)const{return Line(a/k,b/k);}
Po operator*(cLine)const;
Po d()const{return b-a;}DB len2()const{return d().len2();}DB len()const{return d().len();}DB arg()const{return d().arg();}
int sgn(cPo p)const{return dett(a, b, p);}
int sgn(cLine)const;
bool sameSgn(cPo p1,cPo p2)const{return sgn(p1)==sgn(p2);}
void getEquation(DB&K,DB&B)const{
K = ::sgn(a.x, b.x) ? (b.y-a.y)/(b.x-a.x) : OO;
B = a.y - K*a.x;
}
void getEquation(DB&A,DB&B,DB&C)const{A=a.y-b.y,B=b.x-a.x,C=det(a, b);}
Line&push(DB r){ // 正数右手螺旋向里
Po v=d()._1().lt()*r;a+=v,b+=v; rTs;
}
};
inline DB dot(cLine l1,cLine l2){return dot(l1.d(),l2.d());}
inline DB dot(cLine l,cPo p){return dot(l.a,l.b,p);}
inline DB dot(cPo p,cLine l){return dot(p,l.a,l.b);}
inline DB det(cLine l1,cLine l2){return det(l1.d(),l2.d());}
inline DB det(cLine l,cPo p){return det(l.a,l.b,p);}
inline DB det(cPo p,cLine l){return det(p,l.a,l.b);}
inline DB ang(cLine l0,cLine l1){return ang(l0.d(),l1.d());}
inline DB ang(cLine l,cPo p){return ang(l.a,l.b,p);}
inline DB ang(cPo p,cLine l){return ang(p,l.a,l.b);}
inline int Line::sgn(cLine l)const{return dett(Ts, l);}
inline Po Line::operator*(cLine l)const{return a+d()*det(a,l)/det(Ts,l);}
inline Po operator&(cPo p,cLine l){return l*Line(p,p+l.d().lt());}
inline Po operator%(cPo p,cLine l){return p&l*2-p;}
inline Line push(Line l, DB r){return l.push(r);}
struct Seg: public Line{
Seg(cPo a=Po(),cPo b=Po()):Line(a,b){}
Seg(DB x0,DB y0,DB x1,DB y1):Line(x0,y0,x1,y1){}
Seg(cLine l):Line(l){}
Seg(const Po &a,DB alpha):Line(a,alpha){}
Seg(DB A,DB B,DB C):Line(A,B,C){}
inline int sgn(cPo p)const;
inline int sgn(cLine l)const;
inline bool qrt(cSeg l)const;
inline int sgn(cSeg l)const;
};
// -1不相交 0相交（不规范） 1相交（规范）
inline int Seg::sgn(cPo p)const{return -dott(p,a,b);}
inline int Seg::sgn(cLine l)const{return sgn(Ts*l);}
// quick_rejection_test
inline bool Seg::qrt(cSeg l)const{
return min(a.x,b.x)<=max(l.a.x,l.b.x)&&min(l.a.x,l.b.x)<=max(a.x,b.x)&&
min(a.y,b.y)<=max(l.a.y,l.b.y)&&min(l.a.y,l.b.y)<=max(a.y,b.y);
}
inline int Seg::sgn(cSeg l)const{
if (!qrt(l)) return -1;
/*return
(dett(a,b,l.a)*dett(a,b,l.b)<=0 &&
dett(l.a,l.b,a)*dett(l.a,l.b,b)<=0)?1:-1;*/
int d1=dett(a,b,l.a),d2=dett(a,b,l.b),d3=dett(l.a,l.b,a),d4=dett(l.a,l.b,b);
if ((d1^d2)==-2&&(d3^d4)==-2)return 1;
return ((!d1&&dott(l.a-a,l.a-b)<=0)||(!d2&&dott(l.b-a,l.b-b)<=0)||
(!d3&&dott(a-l.a,a-l.b)<=0)||(!d4&&dott(b-l.a,b-l.b)<=0))?0:-1;
}
//inline DB dist2(cLine l,cPo p){return sqr(fabs(dot(lt(l.d()), p-l.a)))/l.len2();}
inline DB dist2(cLine l,cPo p){return sqr(fabs(det(l.d(), p-l.a)))/l.len2();}
inline DB dist2(cLine l1,cLine l2){return dett(l1,l2)?0:dist2(l1,l2.a);}
inline DB dist2(cSeg l,cPo p){
Po pa = p - l.a, pb = p - l.b;
if (dott(l.d(), pa) <= 0) return pa.len2();
if (dott(l.d(), pb) >= 0) return pb.len2();
return dist2(Line(l), p);
}
inline DB dist2(cSeg s,cLine l){
Po v1=s.a-l.a,v2=s.b-l.a;DB d1=det(l.d(),v1),d2=det(l.d(),v2);
return sgn(d1)!=sgn(d2) ? 0 : sqr(min(fabs(d1), fabs(d2)))/l.len2();
}
inline DB dist2(cSeg l1,cSeg l2){
if (~l1.sgn(l2)) return 0;
else return min(dist2(l2,l1.a), dist2(l2,l1.b), dist2(l1,l2.a), dist2(l1,l2.b));
}
template<class T1, class T2> inline DB dist2(const T1& a, const T2& b){
return dist2(b, a);
}
Po getPo(){Po p;p.in();return p;}
Line getLine(){Line l;l.in();return l;}
DB getArea(const VP& P){DB z=0;FOR(i,1,SZ(P))z+=det(P[i-1],P[i]);return z;}
DB getPeri(const VP& P){DB z=0;FOR(i,1,SZ(P))z+=dist(P[i-1],P[i]);return z;}
} using namespace CG;//}
//}
/** I/O Accelerator Interface .. **/ //{
#define g (c=getchar())
#define d isdigit(g)
#define p x=x*10+c-'0'
#define n x=x*10+'0'-c
#define pp l/=10,p
#define nn l/=10,n
template<class T> inline T& RD(T &x){
char c;while(!d);x=c-'0';while(d)p;
return x;
}
template<class T> inline T& RDD(T &x){
char c;while(g,c!='-'&&!isdigit(c));
if (c=='-'){x='0'-g;while(d)n;}
else{x=c-'0';while(d)p;}
return x;
}
inline DB& RF(DB &x){
//scanf("%lf", &x);
char c;while(g,c!='-'&&c!='.'&&!isdigit(c));
if(c=='-')if(g=='.'){x=0;DB l=1;while(d)nn;x*=l;}
else{x='0'-c;while(d)n;if(c=='.'){DB l=1;while(d)nn;x*=l;}}
else if(c=='.'){x=0;DB l=1;while(d)pp;x*=l;}
else{x=c-'0';while(d)p;if(c=='.'){DB l=1;while(d)pp;x*=l;}}
return x;
}
#undef nn
#undef pp
#undef n
#undef p
#undef d
#undef g
inline char* RS(char *s){
//gets(s);
scanf("%s", s);
return s;
}
LL last_ans; int Case; template<class T> inline void OT(const T &x){
//printf("Case #%d: ", ++Case);
//printf("%lld\n", x);
//printf("%.9f\n", x);
printf("%d\n", x);
//cout << x << endl;
//last_ans = x;
}
//}
//}/* .................................................................................................................................. */
const int N = int(1e5) + 9;
char str[N]; uint S[N], A[N];
int n, m, l;
namespace SHash{ // 1-offset
const int Z = 27;
uint P[N];
int h(uint S[], int l, int r){
--l; return S[r]-S[l]*P[r-l];
}
void init(){
P[0] = 1; FOR(i, 1, N) P[i] = P[i-1] * Z;
}
void init(char str[], int n, uint S[]){
REP_1(i, n) S[i] = S[i-1]*Z + (str[i]-'a'+1);
}
} using namespace SHash;
int main(){
#ifndef ONLINE_JUDGE
freopen("in.txt", "r", stdin);
//freopen("out.txt", "w", stdout);
#endif
init(); while (~scanf("%d%d", &m, &l)){
n = strlen(RS(str+1)); init(str, n, S);
int res = 0; REP_1(o, l){
int ll = 0; set<uint> H; REP_1(i, n){
if (o+i*l-1 > n) break; A[i] = h(S, o+(i-1)*l, o+i*l-1);
while (CTN(H, A[i])) H.erase(A[++ll]); H.insert(A[i]);
if (i-ll == m) ++res, H.erase(A[++ll]);
}
}
OT(res);
}
}
Raw
K.cpp
/** Micro Mezz Macro Flation -- Overheated Economy ., Last Update: May. 7th 2014 **/ //{
/** Header .. **/ //{
#pragma comment(linker, "/STACK:36777216")
//#pragma GCC optimize ("O2")
#define LOCAL
//#include "testlib.h"
#include <functional>
#include <algorithm>
#include <iostream>
#include <fstream>
#include <sstream>
#include <iomanip>
#include <numeric>
#include <cstring>
#include <climits>
#include <cassert>
#include <complex>
#include <cstdio>
#include <string>
#include <vector>
#include <bitset>
#include <queue>
#include <stack>
#include <cmath>
#include <ctime>
#include <list>
#include <set>
#include <map>
//#include <tr1/unordered_set>
//#include <tr1/unordered_map>
//#include <array>
using namespace std;
#define REP(i, n) for (int i=0;i<n;++i)
#define FOR(i, a, b) for (int i=a;i<b;++i)
#define DWN(i, b, a) for (int i=b-1;i>=a;--i)
#define REP_1(i, n) for (int i=1;i<=n;++i)
#define FOR_1(i, a, b) for (int i=a;i<=b;++i)
#define DWN_1(i, b, a) for (int i=b;i>=a;--i)
#define REP_C(i, n) for (int n____=n,i=0;i<n____;++i)
#define FOR_C(i, a, b) for (int b____=b,i=a;i<b____;++i)
#define DWN_C(i, b, a) for (int a____=a,i=b-1;i>=a____;--i)
#define REP_N(i, n) for (i=0;i<n;++i)
#define FOR_N(i, a, b) for (i=a;i<b;++i)
#define DWN_N(i, b, a) for (i=b-1;i>=a;--i)
#define REP_1_C(i, n) for (int n____=n,i=1;i<=n____;++i)
#define FOR_1_C(i, a, b) for (int b____=b,i=a;i<=b____;++i)
#define DWN_1_C(i, b, a) for (int a____=a,i=b;i>=a____;--i)
#define REP_1_N(i, n) for (i=1;i<=n;++i)
#define FOR_1_N(i, a, b) for (i=a;i<=b;++i)
#define DWN_1_N(i, b, a) for (i=b;i>=a;--i)
#define REP_C_N(i, n) for (int n____=(i=0,n);i<n____;++i)
#define FOR_C_N(i, a, b) for (int b____=(i=0,b);i<b____;++i)
#define DWN_C_N(i, b, a) for (int a____=(i=b-1,a);i>=a____;--i)
#define REP_1_C_N(i, n) for (int n____=(i=1,n);i<=n____;++i)
#define FOR_1_C_N(i, a, b) for (int b____=(i=a,b);i<=b____;++i)
#define DWN_1_C_N(i, b, a) for (int a____=(i=b,a);i>=a____;--i)
#define ECH(it, A) for (__typeof(A.begin()) it=A.begin(); it != A.end(); ++it)
#define REP_S(i, str) for (char*i=str;*i;++i)
#define REP_L(i, hd, suc) for (int i=hd;i;i=suc[i])
#define REP_G(i, u) REP_L(i,hd[u],suc)
#define REP_SS(x, s) for (int x=s;x;x=(x-1)&s)
#define DO(n) for ( int ____n = n; ____n-->0; )
#define REP_2(i, j, n, m) REP(i, n) REP(j, m)
#define REP_2_1(i, j, n, m) REP_1(i, n) REP_1(j, m)
#define REP_3(i, j, k, n, m, l) REP(i, n) REP(j, m) REP(k, l)
#define REP_3_1(i, j, k, n, m, l) REP_1(i, n) REP_1(j, m) REP_1(k, l)
#define REP_4(i, j, k, ii, n, m, l, nn) REP(i, n) REP(j, m) REP(k, l) REP(ii, nn)
#define REP_4_1(i, j, k, ii, n, m, l, nn) REP_1(i, n) REP_1(j, m) REP_1(k, l) REP_1(ii, nn)
#define ALL(A) A.begin(), A.end()
#define LLA(A) A.rbegin(), A.rend()
#define CPY(A, B) memcpy(A, B, sizeof(A))
#define INS(A, P, B) A.insert(A.begin() + P, B)
#define ERS(A, P) A.erase(A.begin() + P)
#define LBD(A, x) (lower_bound(ALL(A), x) - A.begin())
#define UBD(A, x) (lower_bound(ALL(A), x) - A.begin())
#define CTN(T, x) (T.find(x) != T.end())
#define SZ(A) int((A).size())
#define PB push_back
#define MP(A, B) make_pair(A, B)
#define PTT pair<T, T>
#define Ts *this
#define rTs return Ts
#define fi first
#define se second
#define re real()
#define im imag()
#define Rush for(int ____T=RD(); ____T--;)
#define Display(A, n, m) { \
REP(i, n){ \
REP(j, m-1) cout << A[i][j] << " "; \
cout << A[i][m-1] << endl; \
} \
}
#define Display_1(A, n, m) { \
REP_1(i, n){ \
REP_1(j, m-1) cout << A[i][j] << " "; \
cout << A[i][m] << endl; \
} \
}
typedef long long LL;
//typedef long double DB;
typedef double DB;
typedef unsigned uint;
typedef unsigned long long uLL;
typedef vector<int> VI;
typedef vector<char> VC;
typedef vector<string> VS;
typedef vector<LL> VL;
typedef vector<DB> VF;
typedef set<int> SI;
typedef set<string> SS;
typedef map<int, int> MII;
typedef map<string, int> MSI;
typedef pair<int, int> PII;
typedef pair<LL, LL> PLL;
typedef vector<PII> VII;
typedef vector<VI> VVI;
typedef vector<VII> VVII;
template<class T> inline T& RD(T &);
template<class T> inline void OT(const T &);
//inline int RD(){int x; return RD(x);}
inline LL RD(){LL x; return RD(x);}
inline DB& RF(DB &);
inline DB RF(){DB x; return RF(x);}
inline char* RS(char *s);
inline char& RC(char &c);
inline char RC();
inline char& RC(char &c){scanf(" %c", &c); return c;}
inline char RC(){char c; return RC(c);}
//inline char& RC(char &c){c = getchar(); return c;}
//inline char RC(){return getchar();}
template<class T> inline T& RDD(T &);
inline LL RDD(){LL x; return RDD(x);}
template<class T0, class T1> inline T0& RD(T0 &x0, T1 &x1){RD(x0), RD(x1); return x0;}
template<class T0, class T1, class T2> inline T0& RD(T0 &x0, T1 &x1, T2 &x2){RD(x0), RD(x1), RD(x2); return x0;}
template<class T0, class T1, class T2, class T3> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3){RD(x0), RD(x1), RD(x2), RD(x3); return x0;}
template<class T0, class T1, class T2, class T3, class T4> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4); return x0;}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5); return x0;}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5, T6 &x6){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5), RD(x6); return x0;}
template<class T0, class T1> inline void OT(const T0 &x0, const T1 &x1){OT(x0), OT(x1);}
template<class T0, class T1, class T2> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2){OT(x0), OT(x1), OT(x2);}
template<class T0, class T1, class T2, class T3> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3){OT(x0), OT(x1), OT(x2), OT(x3);}
template<class T0, class T1, class T2, class T3, class T4> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3, const T4 &x4){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3, const T4 &x4, const T5 &x5){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3, const T4 &x4, const T5 &x5, const T6 &x6){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5), OT(x6);}
inline char& RC(char &a, char &b){RC(a), RC(b); return a;}
inline char& RC(char &a, char &b, char &c){RC(a), RC(b), RC(c); return a;}
inline char& RC(char &a, char &b, char &c, char &d){RC(a), RC(b), RC(c), RC(d); return a;}
inline char& RC(char &a, char &b, char &c, char &d, char &e){RC(a), RC(b), RC(c), RC(d), RC(e); return a;}
inline char& RC(char &a, char &b, char &c, char &d, char &e, char &f){RC(a), RC(b), RC(c), RC(d), RC(e), RC(f); return a;}
inline char& RC(char &a, char &b, char &c, char &d, char &e, char &f, char &g){RC(a), RC(b), RC(c), RC(d), RC(e), RC(f), RC(g); return a;}
inline DB& RF(DB &a, DB &b){RF(a), RF(b); return a;}
inline DB& RF(DB &a, DB &b, DB &c){RF(a), RF(b), RF(c); return a;}
inline DB& RF(DB &a, DB &b, DB &c, DB &d){RF(a), RF(b), RF(c), RF(d); return a;}
inline DB& RF(DB &a, DB &b, DB &c, DB &d, DB &e){RF(a), RF(b), RF(c), RF(d), RF(e); return a;}
inline DB& RF(DB &a, DB &b, DB &c, DB &d, DB &e, DB &f){RF(a), RF(b), RF(c), RF(d), RF(e), RF(f); return a;}
inline DB& RF(DB &a, DB &b, DB &c, DB &d, DB &e, DB &f, DB &g){RF(a), RF(b), RF(c), RF(d), RF(e), RF(f), RF(g); return a;}
inline void RS(char *s1, char *s2){RS(s1), RS(s2);}
inline void RS(char *s1, char *s2, char *s3){RS(s1), RS(s2), RS(s3);}
template<class T0,class T1>inline void RDD(T0&a, T1&b){RDD(a),RDD(b);}
template<class T0,class T1,class T2>inline void RDD(T0&a, T1&b, T2&c){RDD(a),RDD(b),RDD(c);}
template<class T> inline void RST(T &A){memset(A, 0, sizeof(A));}
template<class T> inline void FLC(T &A, int x){memset(A, x, sizeof(A));}
template<class T> inline void CLR(T &A){A.clear();}
template<class T0, class T1> inline void RST(T0 &A0, T1 &A1){RST(A0), RST(A1);}
template<class T0, class T1, class T2> inline void RST(T0 &A0, T1 &A1, T2 &A2){RST(A0), RST(A1), RST(A2);}
template<class T0, class T1, class T2, class T3> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3){RST(A0), RST(A1), RST(A2), RST(A3);}
template<class T0, class T1, class T2, class T3, class T4> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5), RST(A6);}
template<class T0, class T1> inline void FLC(T0 &A0, T1 &A1, int x){FLC(A0, x), FLC(A1, x);}
template<class T0, class T1, class T2> inline void FLC(T0 &A0, T1 &A1, T2 &A2, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x);}
template<class T0, class T1, class T2, class T3> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x);}
template<class T0, class T1, class T2, class T3, class T4> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x), FLC(A5, x);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x), FLC(A5, x), FLC(A6, x);}
template<class T> inline void CLR(priority_queue<T, vector<T>, less<T> > &Q){while (!Q.empty()) Q.pop();}
template<class T> inline void CLR(priority_queue<T, vector<T>, greater<T> > &Q){while (!Q.empty()) Q.pop();}
template<class T> inline void CLR(stack<T> &S){while (!S.empty()) S.pop();}
template<class T0, class T1> inline void CLR(T0 &A0, T1 &A1){CLR(A0), CLR(A1);}
template<class T0, class T1, class T2> inline void CLR(T0 &A0, T1 &A1, T2 &A2){CLR(A0), CLR(A1), CLR(A2);}
template<class T0, class T1, class T2, class T3> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3){CLR(A0), CLR(A1), CLR(A2), CLR(A3);}
template<class T0, class T1, class T2, class T3, class T4> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5), CLR(A6);}
template<class T> inline void CLR(T &A, int n){REP(i, n) CLR(A[i]);}
template<class T> inline bool EPT(T &a){return a.empty();}
template<class T> inline T& SRT(T &A){sort(ALL(A)); return A;}
template<class T, class C> inline T& SRT(T &A, C B){sort(ALL(A), B); return A;}
template<class T> inline T& RVS(T &A){reverse(ALL(A)); return A;}
template<class T> inline T& UNQQ(T &A){A.resize(unique(ALL(A))-A.begin());return A;}
template<class T> inline T& UNQ(T &A){SRT(A);return UNQQ(A);}
//}
/** Constant List .. **/ //{
const int MOD = int(1e9) + 7;
const int INF = 0x3f3f3f3f;
const LL INFF = 0x3f3f3f3f3f3f3f3fLL;
const DB EPS = 1e-9;
const DB OO = 1e20;
const DB PI = acos(-1.0); //M_PI;
const int dx[] = {-1, 0, 1, 0};
const int dy[] = {0, 1, 0, -1};
//}
/** Add On .. **/ //{
// <<= '0. Nichi Joo ., //{
template<class T> inline T& checkMin(T &a,const T b){if (b<a) a=b;return a;}
template<class T> inline T& checkMax(T &a,const T b){if (a<b) a=b;return a;}
template<class T> inline T& checkMin(T &a, T &b, const T x){checkMin(a, x), checkMin(b, x);return a;}
template<class T> inline T& checkMax(T &a, T &b, const T x){checkMax(a, x), checkMax(b, x);return a;}
template <class T, class C> inline T& checkMin(T& a, const T b, C c){if (c(b,a)) a = b;return a;}
template <class T, class C> inline T& checkMax(T& a, const T b, C c){if (c(a,b)) a = b;return a;}
template<class T> inline T min(T a, T b, T c){return min(min(a, b), c);}
template<class T> inline T max(T a, T b, T c){return max(max(a, b), c);}
template<class T> inline T min(T a, T b, T c, T d){return min(min(a, b), min(c, d));}
template<class T> inline T max(T a, T b, T c, T d){return max(max(a, b), max(c, d));}
template<class T> inline T min(T a, T b, T c, T d, T e){return min(min(min(a,b),min(c,d)),e);}
template<class T> inline T max(T a, T b, T c, T d, T e){return max(max(max(a,b),max(c,d)),e);}
template<class T> inline T sqr(T a){return a*a;}
template<class T> inline T cub(T a){return a*a*a;}
template<class T> inline T ceil(T x, T y){return (x - 1) / y + 1;}
template<class T> T abs(T x){return x>0?x:-x;}
inline int sgn(DB x){return x < -EPS ? -1 : x > EPS;}
inline int sgn(DB x, DB y){return sgn(x - y);}
inline DB cos(DB a, DB b, DB c){return (sqr(a)+sqr(b)-sqr(c))/(2*a*b);}
inline DB cot(DB x){return 1./tan(x);};
inline DB sec(DB x){return 1./cos(x);};
inline DB csc(DB x){return 1./sin(x);};
//}
// <<= '1. Bitwise Operation ., //{
namespace BO{
inline bool _1(int x, int i){return bool(x&1<<i);}
inline bool _1(LL x, int i){return bool(x&1LL<<i);}
inline LL _1(int i){return 1LL<<i;}
inline LL _U(int i){return _1(i) - 1;};
inline int reverse_bits(int x){
x = ((x >> 1) & 0x55555555) | ((x << 1) & 0xaaaaaaaa);
x = ((x >> 2) & 0x33333333) | ((x << 2) & 0xcccccccc);
x = ((x >> 4) & 0x0f0f0f0f) | ((x << 4) & 0xf0f0f0f0);
x = ((x >> 8) & 0x00ff00ff) | ((x << 8) & 0xff00ff00);
x = ((x >>16) & 0x0000ffff) | ((x <<16) & 0xffff0000);
return x;
}
inline LL reverse_bits(LL x){
x = ((x >> 1) & 0x5555555555555555LL) | ((x << 1) & 0xaaaaaaaaaaaaaaaaLL);
x = ((x >> 2) & 0x3333333333333333LL) | ((x << 2) & 0xccccccccccccccccLL);
x = ((x >> 4) & 0x0f0f0f0f0f0f0f0fLL) | ((x << 4) & 0xf0f0f0f0f0f0f0f0LL);
x = ((x >> 8) & 0x00ff00ff00ff00ffLL) | ((x << 8) & 0xff00ff00ff00ff00LL);
x = ((x >>16) & 0x0000ffff0000ffffLL) | ((x <<16) & 0xffff0000ffff0000LL);
x = ((x >>32) & 0x00000000ffffffffLL) | ((x <<32) & 0xffffffff00000000LL);
return x;
}
template<class T> inline bool odd(T x){return x&1;}
template<class T> inline bool even(T x){return !odd(x);}
template<class T> inline T low_bit(T x) {return x & -x;}
template<class T> inline T high_bit(T x) {T p = low_bit(x);while (p != x) x -= p, p = low_bit(x);return p;}
template<class T> inline T cover_bit(T x){T p = 1; while (p < x) p <<= 1;return p;}
template<class T> inline int cover_idx(T x){int p = 0; while (_1(p) < x ) ++p; return p;}
inline int clz(int x){return __builtin_clz(x);}
inline int clz(LL x){return __builtin_clzll(x);}
inline int ctz(int x){return __builtin_ctz(x);}
inline int ctz(LL x){return __builtin_ctzll(x);}
inline int lg2(int x){return !x ? -1 : 31 - clz(x);}
inline int lg2(LL x){return !x ? -1 : 63 - clz(x);}
inline int low_idx(int x){return !x ? -1 : ctz(x);}
inline int low_idx(LL x){return !x ? -1 : ctz(x);}
inline int high_idx(int x){return lg2(x);}
inline int high_idx(LL x){return lg2(x);}
inline int parity(int x){return __builtin_parity(x);}
inline int parity(LL x){return __builtin_parityll(x);}
inline int count_bits(int x){return __builtin_popcount(x);}
inline int count_bits(LL x){return __builtin_popcountll(x);}
} using namespace BO;//}
// <<= '2. Number Theory .,//{
namespace NT{
inline LL gcd(LL a, LL b){return __gcd(a, b);}
inline LL lcm(LL a, LL b){return a*b/gcd(a,b);}
inline void INC(int &a, int b){a += b; if (a >= MOD) a -= MOD;}
inline int sum(int a, int b){a += b; if (a >= MOD) a -= MOD; return a;}
inline void DEC(int &a, int b){a -= b; if (a < 0) a += MOD;}
inline int dff(int a, int b){a -= b; if (a < 0) a += MOD; return a;}
inline void MUL(int &a, int b){a = (LL)a * b % MOD;}
inline int pdt(int a, int b){return (LL)a * b % MOD;}
inline int gcd(int m, int n, int &x, int &y){
x = 1, y = 0; int xx = 0, yy = 1, q;
while (1){
q = m / n, m %= n;
if (!m){x = xx, y = yy; return n;}
DEC(x, pdt(q, xx)), DEC(y, pdt(q, yy));
q = n / m, n %= m;
if (!n) return m;
DEC(xx, pdt(q, x)), DEC(yy, pdt(q, y));
}
}
inline int sum(int a, int b, int c){return sum(a, sum(b, c));}
inline int sum(int a, int b, int c, int d){return sum(sum(a, b), sum(c, d));}
inline int pdt(int a, int b, int c){return pdt(a, pdt(b, c));}
inline int pdt(int a, int b, int c, int d){return pdt(pdt(a, b), pdt(c, d));}
inline int pow(int a, LL b){
int c(1); while (b){
if (b&1) MUL(c, a);
MUL(a, a), b >>= 1;
}
return c;
}
template<class T> inline T pow(T a, LL b){
T c(1); while (b){
if (b&1) c *= a;
a *= a, b >>= 1;
}
return c;
}
template<class T> inline T pow(T a, int b){
return pow(a, (LL)b);
}
inline int _I(int b){
int a = MOD, x1 = 0, x2 = 1, q;
while (true){
q = a / b, a %= b;
if (!a) return (x2 + MOD) % MOD;
DEC(x1, pdt(q, x2));
q = b / a, b %= a;
if (!b) return (x1 + MOD) % MOD;
DEC(x2, pdt(q, x1));
}
}
inline void DIV(int &a, int b){MUL(a, _I(b));}
inline int qtt(int a, int b){return pdt(a, _I(b));}
struct Int{
int val;
operator int() const{return val;}
Int(int val = 0):val(val){
val %= MOD; if (val < 0) val += MOD;
}
Int(LL _val){
_val %= MOD; if (_val < 0) _val += MOD;
val = _val;
}
Int& operator +=(const int& rhs){
INC(val, rhs);
return *this;
}
Int operator +(const int& rhs) const{
return sum(val, rhs);
}
Int& operator -=(const int& rhs){
DEC(val, rhs);
return *this;
}
Int operator -(const int& rhs) const{
return dff(val, rhs);
}
Int& operator *=(const int& rhs){
MUL(val, rhs);
return *this;
}
Int operator *(const int& rhs) const{
return pdt(val, rhs);
}
Int& operator /=(const int& rhs){
DIV(val, rhs);
return *this;
}
Int operator /(const int& rhs) const{
return qtt(val, rhs);
}
Int operator-()const{
return MOD-*this;
}
};
/*
Int Fact[N], Factt[N]; Int Binom(int n, int m){
return Fact[n] * Factt[m] * Factt[n-m];
}
*/
/*
Fact[0] = 1; REP_1(i, N-1) Fact[i] = Fact[i-1] * i;
Factt[N-1] = _I(Fact[N-1]); DWN(i, N, 1) Factt[i-1] = Factt[i] * i;
*/
/*
int Binom[N][N];
REP(i, N){Binom[i][0] = 1; REP_1(j, i) Binom[i][j] = Binom[i-1][j-1] + Binom[i-1][j];}
*/
/*
const int PMAX = 1;
VI P; bitset<PMAX> isP;
void sieve(){
FOR(i, 2, PMAX){
if (!isP[i]) P.PB(i);
for (int j=0;j<SZ(P)&&i*P[j]<PMAX;++j){
isP[i*P[j]]=1; if (!(i%P[j])) break;
}
}
}
*/
/*
inline int phi(int n){
int res = n; for (int i=2;sqr(i)<=n;++i) if (!(n%i)){
DEC(res, qtt(res, i));
do{n /= i;} while(!(n%i));
}
if (n != 1)
DEC(res, qtt(res, n));
return res;
}
*/
/*LL d, x, y; void exGcd(LL a, LL b){
if(!b) x = 1, y = 0, d = a;
else{
exGcd(b, a%b); LL t = y;
y = x - (a/b)*y, x = t;
}
}*/
} using namespace NT;//}
// <<= '9. Comutational Geometry .,//{
namespace CG{
#define cPo const Po&
#define cLine const Line&
#define cSeg const Seg&
inline DB dist2(DB x,DB y){return sqr(x)+sqr(y);}
struct Po{
DB x,y;Po(DB x=0,DB y=0):x(x),y(y){}
void in(){RF(x,y);}void out(){printf("(%.2f,%.2f)",x,y);}
inline friend istream&operator>>(istream&i,Po&p){return i>>p.x>>p.y;}
inline friend ostream&operator<<(ostream&o,Po p){return o<<"("<<p.x<<", "<<p.y<< ")";}
Po operator-()const{return Po(-x,-y);}
Po&operator+=(cPo p){x+=p.x,y+=p.y;rTs;}Po&operator-=(cPo p){x-=p.x,y-=p.y;rTs;}
Po&operator*=(DB k){x*=k,y*=k;rTs;}Po&operator/=(DB k){x/=k,y/=k;rTs;}
Po&operator*=(cPo p){rTs=Ts*p;}Po&operator/=(cPo p){rTs=Ts/p;}
Po operator+(cPo p)const{return Po(x+p.x,y+p.y);}Po operator-(cPo p)const{return Po(x-p.x,y-p.y);}
Po operator*(DB k)const{return Po(x*k,y*k);}Po operator/(DB k)const{return Po(x/k,y/k);}
Po operator*(cPo p)const{return Po(x*p.x-y*p.y,y*p.x+x*p.y);}Po operator/(cPo p)const{return Po(x*p.x+y*p.y,y*p.x-x*p.y)/p.len2();}
bool operator==(cPo p)const{return!sgn(x,p.x)&&!sgn(y,p.y);};bool operator!=(cPo p)const{return sgn(x,p.x)||sgn(y,p.y);}
bool operator<(cPo p)const{return sgn(x,p.x)<0||!sgn(x,p.x)&&sgn(y,p.y)<0;}bool operator<=(cPo p)const{return sgn(x,p.x)<0||!sgn(x,p.x)&&sgn(y,p.y)<=0;}
bool operator>(cPo p)const{return!(Ts<=p);}bool operator >=(cPo p)const{return!(Ts<p);}
DB len2()const{return dist2(x,y);}DB len()const{return sqrt(len2());}DB arg()const{return atan2(y,x);}
Po&_1(){rTs/=len();}Po&conj(){y=-y;rTs;}Po&lt(){swap(x,y),x=-x;rTs;}Po&rt(){swap(x,y),y=-y;rTs;}
Po&rot(DB a,cPo o=Po()){Ts-=o;Ts*=Po(cos(a),sin(a));rTs+=o;}
};
inline DB dot(DB x1,DB y1,DB x2,DB y2){return x1*x2+y1*y2;}
inline DB dot(cPo a,cPo b){return dot(a.x,a.y,b.x,b.y);}
inline DB dot(cPo p0,cPo p1,cPo p2){return dot(p1-p0,p2-p0);}
inline DB det(DB x1,DB y1,DB x2,DB y2){return x1*y2-x2*y1;}
inline DB det(cPo a,cPo b){return det(a.x,a.y,b.x,b.y);}
inline DB det(cPo p0,cPo p1,cPo p2){return det(p1-p0,p2-p0);}
inline DB ang(cPo p0,cPo p1){return acos(dot(p0,p1)/p0.len()/p1.len());}
inline DB ang(cPo p0,cPo p1,cPo p2){return ang(p1-p0,p2-p0);}
inline DB ang(cPo p0,cPo p1,cPo p2,cPo p3){return ang(p1-p0,p3-p2);}
inline DB dist2(const Po &a, const Po &b){return dist2(a.x-b.x, a.y-b.y);}
template<class T1, class T2> inline int dett(const T1 &x, const T2 &y){return sgn(det(x, y));}
template<class T1, class T2, class T3> inline int dett(const T1 &x, const T2 &y, const T3 &z){return sgn(det(x, y, z));}
template<class T1, class T2, class T3, class T4> inline int dett(const T1 &x, const T2 &y, const T3 &z, const T4 &w){return sgn(det(x, y, z, w));}
template<class T1, class T2> inline int dott(const T1 &x, const T2 &y){return sgn(dot(x, y));}
template<class T1, class T2, class T3> inline int dott(const T1 &x, const T2 &y, const T3 &z){return sgn(dot(x, y, z));}
template<class T1, class T2, class T3, class T4> inline int dott(const T1 &x, const T2 &y, const T3 &z, const T4 &w){return sgn(dot(x, y, z, w));}
template<class T1, class T2> inline DB arg(const T1 &x, const T2 &y){DB a=ang(x,y);return~dett(x,y)?a:2*PI-a;}
template<class T1, class T2, class T3> inline DB arg(const T1 &x, const T2 &y, const T3 &z){DB a=ang(x,y,z);return~dett(x,y,z)?a:2*PI-a;}
template<class T1, class T2, class T3, class T4> inline DB arg(const T1 &x, const T2 &y, const T3 &z, const T4 &w){DB a=ang(x,y,z,w);return~dett(x,y,z,w)?a:2*PI-a;}
template<class T1, class T2> inline DB dist(const T1 &x, const T2 &y){return sqrt(dist2(x, y));}
template<class T1, class T2, class T3> inline DB dist(const T1 &x, const T2 &y, const T3 &z){return sqrt(dist2(x, y, z));}
inline Po _1(Po p){return p._1();}inline Po conj(Po p){return p.conj();}
inline Po lt(Po p){return p.lt();}inline Po rt(Po p){return p.rt();}
inline Po rot(Po p,DB a,cPo o=Po()){return p.rot(a,o);}
inline Po operator *(DB k,cPo p){return p*k;}
inline Po operator /(DB k,cPo p){return conj(p)*k/p.len2();}
typedef vector<Po> VP;
struct Line{
Po a,b;Line(cPo a=Po(),cPo b=Po()):a(a),b(b){}
Line(DB x0,DB y0,DB x1,DB y1):a(Po(x0,y0)),b(Po(x1,y1)){}
Line(cLine l):a(l.a),b(l.b){}
//Ax+By+C=0
Line(DB A,DB B,DB C){
C=-C;if(!::sgn(A))a=Po(0,C/B),b=Po(1,C/B);
else if(!::sgn(B))a=Po(C/A,0),b=Po(C/A,1);
else a=Po(0,C/B),b=Po(1,(C-A)/B);
}
void in(){a.in(),b.in();}
inline friend istream&operator>>(istream&i,Line& p){return i>>p.a>>p.b;}
inline friend ostream&operator<<(ostream&o,Line p){return o<<p.a<<"-"<< p.b;}
Line operator+(cPo x)const{return Line(a+x,b+x);}
Line operator-(cPo x)const{return Line(a-x,b-x);}
Line operator*(DB k)const{return Line(a*k,b*k);}
Line operator/(DB k)const{return Line(a/k,b/k);}
Po operator*(cLine)const;
Po d()const{return b-a;}DB len2()const{return d().len2();}DB len()const{return d().len();}DB arg()const{return d().arg();}
int sgn(cPo p)const{return dett(a, b, p);}
int sgn(cLine)const;
bool sameSgn(cPo p1,cPo p2)const{return sgn(p1)==sgn(p2);}
void getEquation(DB&K,DB&B)const{
K = ::sgn(a.x, b.x) ? (b.y-a.y)/(b.x-a.x) : OO;
B = a.y - K*a.x;
}
void getEquation(DB&A,DB&B,DB&C)const{A=a.y-b.y,B=b.x-a.x,C=det(a, b);}
Line&push(DB r){ // 正数右手螺旋向里
Po v=d()._1().lt()*r;a+=v,b+=v; rTs;
}
};
inline DB dot(cLine l1,cLine l2){return dot(l1.d(),l2.d());}
inline DB dot(cLine l,cPo p){return dot(l.a,l.b,p);}
inline DB dot(cPo p,cLine l){return dot(p,l.a,l.b);}
inline DB det(cLine l1,cLine l2){return det(l1.d(),l2.d());}
inline DB det(cLine l,cPo p){return det(l.a,l.b,p);}
inline DB det(cPo p,cLine l){return det(p,l.a,l.b);}
inline DB ang(cLine l0,cLine l1){return ang(l0.d(),l1.d());}
inline DB ang(cLine l,cPo p){return ang(l.a,l.b,p);}
inline DB ang(cPo p,cLine l){return ang(p,l.a,l.b);}
inline int Line::sgn(cLine l)const{return dett(Ts, l);}
inline Po Line::operator*(cLine l)const{return a+d()*det(a,l)/det(Ts,l);}
inline Po operator&(cPo p,cLine l){return l*Line(p,p+l.d().lt());}
inline Po operator%(cPo p,cLine l){return p&l*2-p;}
inline Line push(Line l, DB r){return l.push(r);}
struct Seg: public Line{
Seg(cPo a=Po(),cPo b=Po()):Line(a,b){}
Seg(DB x0,DB y0,DB x1,DB y1):Line(x0,y0,x1,y1){}
Seg(cLine l):Line(l){}
Seg(const Po &a,DB alpha):Line(a,alpha){}
Seg(DB A,DB B,DB C):Line(A,B,C){}
inline int sgn(cPo p)const;
inline int sgn(cLine l)const;
inline bool qrt(cSeg l)const;
inline int sgn(cSeg l)const;
};
// -1不相交 0相交（不规范） 1相交（规范）
inline int Seg::sgn(cPo p)const{return -dott(p,a,b);}
inline int Seg::sgn(cLine l)const{return sgn(Ts*l);}
// quick_rejection_test
inline bool Seg::qrt(cSeg l)const{
return min(a.x,b.x)<=max(l.a.x,l.b.x)&&min(l.a.x,l.b.x)<=max(a.x,b.x)&&
min(a.y,b.y)<=max(l.a.y,l.b.y)&&min(l.a.y,l.b.y)<=max(a.y,b.y);
}
inline int Seg::sgn(cSeg l)const{
if (!qrt(l)) return -1;
/*return
(dett(a,b,l.a)*dett(a,b,l.b)<=0 &&
dett(l.a,l.b,a)*dett(l.a,l.b,b)<=0)?1:-1;*/
int d1=dett(a,b,l.a),d2=dett(a,b,l.b),d3=dett(l.a,l.b,a),d4=dett(l.a,l.b,b);
if ((d1^d2)==-2&&(d3^d4)==-2)return 1;
return ((!d1&&dott(l.a-a,l.a-b)<=0)||(!d2&&dott(l.b-a,l.b-b)<=0)||
(!d3&&dott(a-l.a,a-l.b)<=0)||(!d4&&dott(b-l.a,b-l.b)<=0))?0:-1;
}
//inline DB dist2(cLine l,cPo p){return sqr(fabs(dot(lt(l.d()), p-l.a)))/l.len2();}
inline DB dist2(cLine l,cPo p){return sqr(fabs(det(l.d(), p-l.a)))/l.len2();}
inline DB dist2(cLine l1,cLine l2){return dett(l1,l2)?0:dist2(l1,l2.a);}
inline DB dist2(cSeg l,cPo p){
Po pa = p - l.a, pb = p - l.b;
if (dott(l.d(), pa) <= 0) return pa.len2();
if (dott(l.d(), pb) >= 0) return pb.len2();
return dist2(Line(l), p);
}
inline DB dist2(cSeg s,cLine l){
Po v1=s.a-l.a,v2=s.b-l.a;DB d1=det(l.d(),v1),d2=det(l.d(),v2);
return sgn(d1)!=sgn(d2) ? 0 : sqr(min(fabs(d1), fabs(d2)))/l.len2();
}
inline DB dist2(cSeg l1,cSeg l2){
if (~l1.sgn(l2)) return 0;
else return min(dist2(l2,l1.a), dist2(l2,l1.b), dist2(l1,l2.a), dist2(l1,l2.b));
}
template<class T1, class T2> inline DB dist2(const T1& a, const T2& b){
return dist2(b, a);
}
Po getPo(){Po p;p.in();return p;}
Line getLine(){Line l;l.in();return l;}
DB getArea(const VP& P){DB z=0;FOR(i,1,SZ(P))z+=det(P[i-1],P[i]);return z;}
DB getPeri(const VP& P){DB z=0;FOR(i,1,SZ(P))z+=dist(P[i-1],P[i]);return z;}
} using namespace CG;//}
//}
/** I/O Accelerator Interface .. **/ //{
#define g (c=getchar())
#define d isdigit(g)
#define p x=x*10+c-'0'
#define n x=x*10+'0'-c
#define pp l/=10,p
#define nn l/=10,n
template<class T> inline T& RD(T &x){
char c;while(!d);x=c-'0';while(d)p;
return x;
}
template<class T> inline T& RDD(T &x){
char c;while(g,c!='-'&&!isdigit(c));
if (c=='-'){x='0'-g;while(d)n;}
else{x=c-'0';while(d)p;}
return x;
}
inline DB& RF(DB &x){
//scanf("%lf", &x);
char c;while(g,c!='-'&&c!='.'&&!isdigit(c));
if(c=='-')if(g=='.'){x=0;DB l=1;while(d)nn;x*=l;}
else{x='0'-c;while(d)n;if(c=='.'){DB l=1;while(d)nn;x*=l;}}
else if(c=='.'){x=0;DB l=1;while(d)pp;x*=l;}
else{x=c-'0';while(d)p;if(c=='.'){DB l=1;while(d)pp;x*=l;}}
return x;
}
#undef nn
#undef pp
#undef n
#undef p
#undef d
#undef g
inline char* RS(char *s){
//gets(s);
scanf("%s", s);
return s;
}
LL last_ans; int Case; template<class T> inline void OT(const T &x){
//printf("Case #%d: ", ++Case);
//printf("%lld\n", x);
//printf("%.3f\n", x);
printf("%d\n", x);
//cout << x << endl;
//last_ans = x;
}
//}
//}/* .................................................................................................................................. */
const int N = int(1e5)+9, M = 2*N, LV = 18;
int hd[N], suc[M], to[M];
int ST[LV+1][M], sz[N], fa[N][LV], st[N], dep[N];
int n, tt;
inline bool elder(int a, int b){
return dep[a] < dep[b];
}
inline int lca(int a, int b){
int l = st[a], r = st[b]; if (l > r) swap(l, r); ++r; int lv = lg2(r-l);
return min(ST[lv][l], ST[lv][r-(1<<lv)], elder);
}
bool isa(int u1, int u2){
return lca(u1, u2) == u1;
}
int entry(int x, int y, int w){
int xy = lca(x, y); if (!isa(xy, w)) return xy; int xw = lca(x, w);
return xw != xy ? xw : lca(y, w);
}
inline int d(int x, int y){
return dep[x]+dep[y]-2*dep[lca(x,y)];
}
inline int up(int x, int t){
for (int i=0;i<LV&&t;++i,t>>=1)
if (t&1) x = fa[x][i];
return x;
}
#define aa to[i^1]
#define bb to[i]
#define v bb
void dfs(int u = 1){
ST[0][st[u] = ++tt] = u, sz[u] = 1;
REP_G(i, u) if (!st[v]){
dep[v] = dep[u] + 1, fa[v][0] = u; FOR(lv, 1, LV) fa[v][lv] = fa[fa[v][lv-1]][lv-1];
dfs(v), ST[0][++tt] = u, sz[u] += sz[v];
}
}
#undef v
int ans[N], m;
bool cmp(int a, int b){
return d(a, m) < d(b, m);
}
void gao(int x, int y){
int z = lca(x,y), dx = dep[x]-dep[z], dy = dep[y]-dep[z], dd = dx+dy;
int d = dd/2; if (d>=dx) swap(x, y), swap(dx, dy); int m = up(x,d);
if (dd&1) ans[x] = sz[m], ans[y] = n-ans[x];
else ans[x] = sz[up(x,d-1)], ans[y] = d==dx?sz[up(y,d-1)]:n-sz[m];
}
void gao(int u0, int u1, int u2){
gao(u1, u2); int g = n-ans[u1]-ans[u2]; gao(u0, u1);
ans[u1] -= ans[u2]+g;
}
int main(){
#ifndef ONLINE_JUDGE
freopen("in.txt", "r", stdin);
//freopen("out.txt", "w", stdout);
#endif
int __size__ = 256 << 20; // 256MB
char *__p__ = (char*)malloc(__size__) + __size__;
__asm__("movl %0, %%esp\n" :: "r"(__p__));
Rush{
FOR_C(i, 2, RD(n)<<1){
RD(aa, bb);
suc[i] = hd[aa], hd[aa] = i, ++i;
suc[i] = hd[aa], hd[aa] = i;
}
dfs();
for ( int lv = 1 ; (1 << lv) <= tt ; lv ++ ){
for ( int i = 1 ; i + (1 << lv) <= tt + 1 ; i ++ )
ST[lv][i] = min(ST[lv-1][i], ST[lv-1][i + (1<<(lv-1))], elder);
}
Rush{
int u0, u1, u2; RD(u0, u1, u2);
VI I; I.PB(u0), I.PB(u1), I.PB(u2); SRT(I, elder);
#define u0 I[0]
#define u1 I[1]
#define u2 I[2]
if (isa(u0, u1) && isa(u1, u2)){
gao(u0, u1, u2); // Case 1
}
else{
m = entry(u0, u1, u2); SRT(I, cmp);
if (d(u0,m) < d(u1,m)){ // Case 2.1
gao(u1, u0); int g1 = n-ans[u0]-ans[u1];
gao(u0, u2); int g2 = n-ans[u0]-ans[u2];
ans[u0] = n-ans[u1]-ans[u2]-g1-g2;
}
else{ // Case 2.2
gao(u0, u2), gao(u0, u1);
}
}
#undef u0
#undef u1
#undef u2
printf("%d %d %d\n", ans[u0], ans[u1], ans[u2]);
}
fill(hd+1, hd+n+1, 0);
fill(st+1, st+n+1, 0);
tt = 0;
}
}
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