短版头文件.cpp

#include <type_traits>
#include <cstdint>
#include <iostream>
#include <fstream>
#include <iomanip>
#include <vector>
#include <queue>
#include <functional>
#include <numeric>
#include <cassert>
#include <climits>
using namespace std;

// tourist's modular-arithmetic class
template<typename T>
T inverse(T a, T m) {
  T u = 0, v = 1;
  while (a != 0) {
    T t = m / a;
    m -= t * a;
    swap(a, m);
    u -= t * v;
    swap(u, v);
  }
  assert(m == 1);
  return u;
}

template<typename T>
class Modular {
public:
  using Type = typename decay<decltype(T::value)>::type;

  constexpr Modular() : value() {}

  template<typename U>
  Modular(const U &x) {
    value = normalize(x);
  }

  template<typename U>
  static Type normalize(const U &x) {
    Type v;
    if (-mod() <= x && x < mod()) v = static_cast<Type>(x);
    else v = static_cast<Type>(x % mod());
    if (v < 0) v += mod();
    return v;
  }

  const Type &operator()() const { return value; }

  template<typename U>
  explicit operator U() const { return static_cast<U>(value); }

  constexpr static Type mod() { return T::value; }

  Modular &operator+=(const Modular &other) {
    if ((value += other.value) >= mod()) value -= mod();
    return *this;
  }

  Modular &operator-=(const Modular &other) {
    if ((value -= other.value) < 0) value += mod();
    return *this;
  }

  template<typename U>
  Modular &operator+=(const U &other) { return *this += Modular(other); }

  template<typename U>
  Modular &operator-=(const U &other) { return *this -= Modular(other); }

  Modular &operator++() { return *this += 1; }

  Modular &operator--() { return *this -= 1; }

  Modular operator++(int) {
    Modular result(*this);
    *this += 1;
    return result;
  }

  Modular operator--(int) {
    Modular result(*this);
    *this -= 1;
    return result;
  }

  Modular operator-() const { return Modular(-value); }

  template<typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, int>::value, Modular>::type &operator*=(const Modular &rhs) {
#ifdef _WIN32
    uint64_t x = static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value);
    uint32_t xh = static_cast<uint32_t>(x >> 32), xl = static_cast<uint32_t>(x), d, m;
    asm(
    "divl %4; \n\t"
    : "=a" (d), "=d" (m)
    : "d" (xh), "a" (xl), "r" (mod())
    );
    value = m;
#else
    value = normalize(static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value));
#endif
    return *this;
  }

  template<typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, int64_t>::value, Modular>::type &
  operator*=(const Modular &rhs) {
    int64_t q = static_cast<int64_t>(static_cast<long double>(value) * rhs.value / mod());
    value = normalize(value * rhs.value - q * mod());
    return *this;
  }

  template<typename U = T>
  typename enable_if<!is_integral<typename Modular<U>::Type>::value, Modular>::type &operator*=(const Modular &rhs) {
    value = normalize(value * rhs.value);
    return *this;
  }

  Modular &operator/=(const Modular &other) { return *this *= Modular(inverse(other.value, mod())); }

  template<typename U>
  friend const Modular<U> &abs(const Modular<U> &v) { return v; }

  template<typename U>
  friend bool operator==(const Modular<U> &lhs, const Modular<U> &rhs);

  template<typename U>
  friend bool operator<(const Modular<U> &lhs, const Modular<U> &rhs);

  template<typename U>
  friend std::istream &operator>>(std::istream &stream, Modular<U> &number);

private:
  Type value;
};


template<typename T>
bool operator==(const Modular<T> &lhs, const Modular<T> &rhs) { return lhs.value == rhs.value; }

template<typename T, typename U>
bool operator==(const Modular<T> &lhs, U rhs) { return lhs == Modular<T>(rhs); }

template<typename T, typename U>
bool operator==(U lhs, const Modular<T> &rhs) { return Modular<T>(lhs) == rhs; }

template<typename T>
bool operator!=(const Modular<T> &lhs, const Modular<T> &rhs) { return !(lhs == rhs); }

template<typename T, typename U>
bool operator!=(const Modular<T> &lhs, U rhs) { return !(lhs == rhs); }

template<typename T, typename U>
bool operator!=(U lhs, const Modular<T> &rhs) { return !(lhs == rhs); }

template<typename T>
bool operator<(const Modular<T> &lhs, const Modular<T> &rhs) { return lhs.value < rhs.value; }

template<typename T>
Modular<T> operator+(const Modular<T> &lhs, const Modular<T> &rhs) { return Modular<T>(lhs) += rhs; }

template<typename T, typename U>
Modular<T> operator+(const Modular<T> &lhs, U rhs) { return Modular<T>(lhs) += rhs; }

template<typename T, typename U>
Modular<T> operator+(U lhs, const Modular<T> &rhs) { return Modular<T>(lhs) += rhs; }

template<typename T>
Modular<T> operator-(const Modular<T> &lhs, const Modular<T> &rhs) { return Modular<T>(lhs) -= rhs; }

template<typename T, typename U>
Modular<T> operator-(const Modular<T> &lhs, U rhs) { return Modular<T>(lhs) -= rhs; }

template<typename T, typename U>
Modular<T> operator-(U lhs, const Modular<T> &rhs) { return Modular<T>(lhs) -= rhs; }

template<typename T>
Modular<T> operator*(const Modular<T> &lhs, const Modular<T> &rhs) { return Modular<T>(lhs) *= rhs; }

template<typename T, typename U>
Modular<T> operator*(const Modular<T> &lhs, U rhs) { return Modular<T>(lhs) *= rhs; }

template<typename T, typename U>
Modular<T> operator*(U lhs, const Modular<T> &rhs) { return Modular<T>(lhs) *= rhs; }

template<typename T>
Modular<T> operator/(const Modular<T> &lhs, const Modular<T> &rhs) { return Modular<T>(lhs) /= rhs; }

template<typename T, typename U>
Modular<T> operator/(const Modular<T> &lhs, U rhs) { return Modular<T>(lhs) /= rhs; }

template<typename T, typename U>
Modular<T> operator/(U lhs, const Modular<T> &rhs) { return Modular<T>(lhs) /= rhs; }

template<typename T, typename U>
Modular<T> power(const Modular<T> &a, const U &b) {
  assert(b >= 0);
  Modular<T> x = a, res = 1;
  U p = b;
  while (p > 0) {
    if (p & 1) res *= x;
    x *= x;
    p >>= 1;
  }
  return res;
}

template<typename T>
bool IsZero(const Modular<T> &number) {
  return number() == 0;
}

template<typename T>
string to_string(const Modular<T> &number) {
  return to_string(number());
}

template<typename T>
std::ostream &operator<<(std::ostream &stream, const Modular<T> &number) {
  return stream << number();
}

template<typename T>
std::istream &operator>>(std::istream &stream, Modular<T> &number) {
  typename common_type<typename Modular<T>::Type, int64_t>::type x;
  stream >> x;
  number.value = Modular<T>::normalize(x);
  return stream;
}

struct fast_ios {
  fast_ios() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
  };
} fast_ios_;

#define LSON(x) ((x) * 2)
#define RSON(x) ((x) * 2 + 1)

template<typename A, typename B>
bool chkmin(A &a, const B &b) {
  if (b < a) {
    a = b;
    return true;
  }
  return false;
}

template<typename A, typename B>
bool chkmax(A &a, const B &b) {
  if (b > a) {
    a = b;
    return true;
  }
  return false;
}

int cas;

ostream &kase() {
  return cout << "Case #" << ++cas << ": ";
}

#if __cplusplus < 201402L
template<class Iterator>
std::reverse_iterator<Iterator> make_reverse_iterator(Iterator it) {
    return std::reverse_iterator<Iterator>(it);
}
#endif

template<typename iter_t>
struct iter_pair {
  iter_t _beg, _end;

  iter_t begin() { return _beg; }

  iter_t end() { return _end; }
};

template<class cont>
iter_pair<reverse_iterator<decltype(begin(declval<cont>()))>>
reverse(cont &&r) {
  return {make_reverse_iterator(end(r)), make_reverse_iterator(begin(r))};
}


template<typename T>
void dprintln(const T &t) { cout << t << endl; } // for debug use
template<typename T, typename ...Args>
void dprintln(const T &t, const Args &...rest) {
  cout << t << ' ';
  dprintln(rest...);
}

template<typename T>
ostream &operator<<(ostream &stream, const vector<T> &vec) {
  if (!vec.empty()) {
    stream << vec[0];
    for (size_t i = 1; i < vec.size(); ++i)
      stream << ' ' << vec[i];
  }
  return stream;
}

template<typename T>
void print(const vector<T> &t) { cout << t << '\n'; }

template<typename T>
void print(const T &t) { cout << t << ' '; }

template<typename T, typename ...Args>
void print(const T &t, const Args &...rest) {
  print(t);
  print(rest...);
}

template<typename T>
void println(const T &t) { cout << t << '\n'; }

template<typename T, typename ...Args>
void println(const T &t, const Args &...rest) {
  print(t);
  println(rest...);
}

// this overload is chosen when there's only one argument
template<class T>
void scan(T &t) { cin >> t; }

template<class T, class ...Args>
void scan(T &a, Args &...rest) {
  cin >> a;
  scan(rest...);
}

template<typename T>
istream &operator>>(istream &stream, vector<T> &vec) {
  for (auto &x : vec) stream >> x;
  return stream;
}

using ull = unsigned long long;
using ll = long long;
using ul = unsigned long;
using vl = vector<ll>;
using vi = vector<int>;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pip = pair<int, pii>;
using pll = pair<ll, ll>;
using vb = vector<bool>;
using vpii = vector<pii>;
using ldb = long double;

template<typename int_t>
inline int_t lowbit(int_t x) { return x & -x; }

#define rng(i, a, b) for(int i = (int)(a); i < (int)(b); ++i)
#define up(i, a, b) for (int i = int(a); i <= int(b); ++i)
#define down(i, b, a) for (int i = int(b); i >= int(a); i--)
#define rep(n) for(int _iter_##n = 0, _num_##n = (int)n; _iter_##n < _num_##n; ++_iter_##n)
#define stp(i, a, b, c) for (int i = (a); i < (b); i += (c))
#define FOR(x, cont) for (const auto &x: cont)
#define For(x, cont) for (auto &x: cont)
#define all(x) begin(x), end(x)
#define pb push_back
#define mp make_pair
#define eb emplace_back
#define ep emplace
#define SZ(x) (int)(x).size()
#define UP(i, l, r) for(i = decltype(i)(l); i <= decltype(i)(r); ++i)
#define DOWN(i, r, l) for (i = decltype(i)(r); i >= decltype(i)(l); --i)
template<typename T, typename Comp = less<T>>
using pq = priority_queue<T, vector<T>, Comp>;
#define popcnt(x) __builtin_popcountll((x))
#define SET(arr, v) memset(arr, (v), sizeof (arr))
#define UNIQ(vec) (vec).erase(unique(all(vec)), end(vec))
#define LB(cont, x) int(lower_bound(all(cont), x) - begin(cont))
#define UB(cont, x) int(upper_bound(all(cont), x) - begin(cont))
#define AI(name, n, m) vv<int> name(n, vi(m));
#define AL(name, n, m) vv<ll> name(size_t(n), vl(size_t(m)));
#define AT(T, n, m, a)  vector<vector<T>> a(n, vector<T>(m))
const int dx[] = {0, 0, -1, 1}, dy[] = {-1, 1, 0, 0};
const int dx8[] = {-1, -1, -1, 0, 0, 1, 1, 1}, dy8[] = {-1, 0, 1, -1, 1, -1, 0, 1};
auto bet = [](const ll x, const ll y, const ll i) {
  return x <= i && i <= y;
};

template<typename T1, typename T2>
T1 ceil(T1 x, T2 y) { // y >= 1，是整数。需要注意 x + y - 1 是否会溢出
  return (x + y - 1) / y;
}
#ifdef _MSC_VER
#include <intrin.h>
static inline int __builtin_clzll(unsigned long long x) {
  return (int)__lzcnt64(x);
}
#endif
inline int h_bit(unsigned long long x) {
  return (int) sizeof(unsigned long long) * 8 - 1 - __builtin_clzll(x);
}
// round up to power of 2
unsigned long long pow2(unsigned long long x) {
  return 1ULL << (h_bit(x) + (x != lowbit(x)));
}

template<typename T>
struct BIT {
  vector<T> a;
  function<T(T, T)> bin_op;
  const T init;

  explicit BIT(int n, function<T(T, T)> bin_op, T init = T()) : bin_op(bin_op), init(init) {
    a.assign(n + 1, init);
  }

  T prefix(int x) {
    auto res = init;
    while (x) {
      res = bin_op(a[x], res);
      x -= x & -x;
    }
    return res;
  }

  void modify(int x, T v) {
    while (x < (int) a.size()) {
      a[x] = bin_op(a[x], v);
      x += x & -x;
    }
  }

  void clear() {
    fill(a.begin(), a.end(), init);
  }
};

vi get_prime(int n) {
  vi minp((ul) n + 1), p;
  for (int i = 2; i <= n; i++) {
    if (!minp[i]) {
      minp[i] = i;
      p.pb(i);
    }
    FOR(x, p) {
      if (x <= minp[i] && x * i <= n)
        minp[x * i] = x;
      else break;
    }
  }
  return p;
}

// alias templates
template<typename T> using vv = vector<vector<T>>;
template<typename T1, typename T2 = T1> using vp = vector<pair<T1, T2>>;
template<typename T, int n> using va = vector<array<T, n>>;

//order_of_key (k) : Number of items strictly smaller than k .
//find_by_order(k) : K-th element in a set (counting from zero).
#ifdef __GNUC__
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
template<typename T, typename comp = less<T>>
using rank_tree = __gnu_pbds::tree<
        T,
        __gnu_pbds::null_type,
        comp,
        __gnu_pbds::rb_tree_tag,
        __gnu_pbds::tree_order_statistics_node_update>;
#include <ext/pb_ds/trie_policy.hpp>
using trie = __gnu_pbds::trie<string,__gnu_pbds::null_type>;
#endif

//并查集
struct UnionFind {
  vi par, sz;
  int n_tree;

  explicit UnionFind(int n) : sz(n, 1), n_tree(n) { //0-indexed
    sz.resize(n);
    iota(par.begin(), par.end(), 0);
  }

  int n_cluster() const {
    return n_tree;
  }

  int size(int x) {
    return sz[root(x)];
  }

  int root(int x) {
    return x == par[x] ? x : par[x] = root(par[x]);
  }

  bool unite(int x, int y) {
    int rx = root(x), ry = root(y);
    if (rx != ry) {
      par[rx] = ry;
      --n_tree;
      sz[ry] += sz[rx];
      return true;
    }
    return false;
  }

  bool is_root(int x) const {
    return par[x] == x;
  }
};

template<typename T, typename Compare = std::less<T>>
struct SparseTable {
  size_t n{}; // 0-indexed
  vv<T> a;

  template<typename ptr_t>
  SparseTable(ptr_t beg, ptr_t end):n(end - beg) {
    a.resize((size_t) h_bit(n) + 1); // 注意：不能写成 h_bit(n)
    a[0].assign(beg, end);
    rng (i, 0, SZ(a) - 1) {
      a[i + 1].resize(n);
      rng(j, 0, n - (1u << i)) {
        a[i + 1][j] = min(a[i][j], a[i][j + (1u << i)], Compare());
      }
      rng(j, n - (1u << i), n) {
        a[i + 1][j] = a[i][j];
      }
    }
  }

  using idx_t = long;

  T query(idx_t l, idx_t r) { // l <=  r
    int i = h_bit(r - l + 1ul);
    return min(a[i][l], a[i][r + 1 - (1u << i)], Compare());
  }
};

// debug code by tourist
string to_string(const string &s) {
  return '"' + s + '"';
}

string to_string(const char *s) {
  return to_string((string) s);
}

string to_string(bool b) {
  return (b ? "true" : "false");
}

template<typename A, typename B>
string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}

template<typename A>
string to_string(A v) {
  bool first = true;
  string res = "{";
  for (const auto &x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}

void debug_out() { cerr << endl; }

template<typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}

#ifdef LOCAL
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif
// end DEBUG

template<typename T>
struct Binom {
  vector<T> fact, inv_fact;

  explicit Binom(int n) : fact(n + 1), inv_fact(n + 1) {
    fact[0] = 1;
    up (i, 1, n) fact[i] = fact[i - 1] * i;
    inv_fact[n] = 1 / fact[n];
    down (i, n, 1) {
      inv_fact[i - 1] = inv_fact[i] * i;
    }
  }

  T get_binom(int x, int y) const {
    assert(x <= SZ(fact) - 1);
    assert(x >= 0 && y >= 0);
    if (x < y) return 0;
    return fact[x] * inv_fact[y] * inv_fact[x - y];
  }

  T get_fact(int n) const {
    assert(n < SZ(fact));
    return fact[n];
  }
};

//https://codeforces.com/blog/entry/22072
struct HLD {
  HLD(int n, const int *heavy_son, const int *fa, const int *depth) : top(n + 1), pos(n + 1), depth(depth), fa(fa) {
    int index = 0;
    // 节点编号从1开始
    for (int i = 1; i <= n; i++) {
      if (i != heavy_son[fa[i]]) {
        for (int j = i; j != 0; j = heavy_son[j]) {
          top[j] = i;
          pos[j] = ++index; // pos从1开始
        }
      }
    }
  }

  template<typename BinOpr>
  //返回值是 LCA(u,v)
  int process_path(int u, int v, BinOpr op, bool value_on_edge = false) const {
    while (top[u] != top[v]) {
      if (depth[top[u]] < depth[top[v]]) swap(u, v);
      op(pos[top[u]], pos[u]);
      u = fa[top[u]];
    }
    if (depth[u] > depth[v]) swap(u, v);
    op(pos[u] + value_on_edge, pos[v]);
    return u;
  }

  vector<int> top, pos;
  const int *depth, *fa;
};

template<typename T>
T get_mid(T l, T r) {
  assert(l <= r);
  return l + (r - l) / 2;
}

template<typename T>
int get_bit(T a, int i) {
  return a >> i & 1;
}

/*using ModType = int;

struct VarMod {
  static ModType value;
};
ModType VarMod::value;
ModType &md = VarMod::value;
using Mint = Modular<VarMod>;*/
constexpr int md = 1000000007;
using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;