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#include <stdio.h>
#include <vector>
#include <algorithm>
using namespace std;
#define ll long long
int gcd(int a, int b){
int m = 1;
#include <stdio.h>
#include <memory.h>
#define mod 1000000000
int dp[203][203];
int dy(int s, int k){
if (!k){
if(!s)return 1;
return 0;
#include <stdio.h>
#include <memory.h>
#include <vector>
#include <algorithm>
using namespace std;
#define ll long long
#include <stdio.h>
#include <algorithm>
using namespace std;
int goal;
int lim;
int a[23];
int n;
#include <stdio.h>
#include <limits.h>
#include <algorithm>
#define ll long long
using namespace std;
class ele{
public:
#include <stdio.h>
#include <algorithm>
using namespace std;
int a[10003][2];
int dp[10003][4][4];
int n, m;
#include <stdio.h>
#include <vector>
#include <queue>
#include <string>
#include <map>
using namespace std;
class ele {
public:
#include <stdio.h>
#include <string.h>
#include <algorithm>
using namespace std;
char ptn[103];
char str[103];
int dp[103][103];
#include <stdio.h>
int k, n;
double dp[13][103];
double dy(int c, int s) {
if (s == n)return 1.0;
if (dp[c][s] >= 0)return dp[c][s];
#include <stdio.h>
#include <vector>
#include <queue>
using namespace std;
int o[503]; // orginal
int in[503];
bool win[503][503];