verify/modint/LC_binomial_coefficient.test.cpp

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• Last update: 2026-08-11 23:01:09+09:00
• Problem: https://judge.yosupo.jp/problem/binomial_coefficient

Depends on

• math/barrett.hpp
• 一般 mod での二項係数 (modint/binomial-general-mod.hpp)
• template/debug.hpp
• template/inout.hpp
• template/macro.hpp
• template/template.hpp
• template/util.hpp

Code

#define PROBLEM "https://judge.yosupo.jp/problem/binomial_coefficient"

#include "template/template.hpp"
#include "modint/binomial-general-mod.hpp"

int main() {
  int t, m;
  in(t, m);
  BinomialGeneralMod binom(m);
  while (t--) {
    ll n, k;
    in(n, k);
    out(binom.binom(n, k));
  }
}

#line 1 "verify/modint/LC_binomial_coefficient.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/binomial_coefficient"

#line 2 "template/template.hpp"
#include <bits/stdc++.h>
using namespace std;

#line 2 "template/macro.hpp"
#define rep(i, a, b) for (int i = (a); i < (int)(b); i++)
#define rrep(i, a, b) for (int i = (int)(b) - 1; i >= (a); i--)
#define ALL(v) (v).begin(), (v).end()
#define UNIQUE(v) sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end())
#define SZ(v) (int)v.size()
#define MIN(v) *min_element(ALL(v))
#define MAX(v) *max_element(ALL(v))
#define LB(v, x) int(lower_bound(ALL(v), (x)) - (v).begin())
#define UB(v, x) int(upper_bound(ALL(v), (x)) - (v).begin())
#define YN(b) cout << ((b) ? "YES" : "NO") << "\n";
#define Yn(b) cout << ((b) ? "Yes" : "No") << "\n";
#define yn(b) cout << ((b) ? "yes" : "no") << "\n";
#line 6 "template/template.hpp"

#line 2 "template/util.hpp"
using uint = unsigned int;
using ll = long long int;
using ull = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
template <class T>
using priority_queue_asc = priority_queue<T, vector<T>, greater<T>>;

template <class T, class S = T>
S SUM(const vector<T>& a) {
  return accumulate(ALL(a), S(0));
}
template <class T1, class T2>
inline bool chmin(T1& a, T2 b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T1, class T2>
inline bool chmax(T1& a, T2 b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T1, class T2>
inline bool chmin_opt(optional<T1>& a, T2 b) {
  if (!a || a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T1, class T2>
inline bool chmax_opt(optional<T1>& a, T2 b) {
  if (!a || a < b) {
    a = b;
    return true;
  }
  return false;
}

template <class T>
int popcnt(T x) {
  return __builtin_popcountll(x);
}
template <class T>
int topbit(T x) {
  return (x == 0 ? -1 : 63 - __builtin_clzll(x));
}
template <class T>
int lowbit(T x) {
  return (x == 0 ? -1 : __builtin_ctzll(x));
}
#line 8 "template/template.hpp"

#line 2 "template/inout.hpp"
struct Fast {
  Fast() {
    cin.tie(nullptr);
    ios_base::sync_with_stdio(false);
    cout << fixed << setprecision(15);
  }
} fast;

ostream& operator<<(ostream& os, __uint128_t x) {
  char buf[40];
  size_t k = 0;
  while (x > 0) buf[k++] = (char)(x % 10 + '0'), x /= 10;
  if (k == 0) buf[k++] = '0';
  while (k) os << buf[--k];
  return os;
}
ostream& operator<<(ostream& os, __int128_t x) {
  return x < 0 ? (os << '-' << (__uint128_t)(-x)) : (os << (__uint128_t)x);
}
template <class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N>& a);
template <class T1, class T2>
istream& operator>>(istream& is, pair<T1, T2>& p) {
  return is >> p.first >> p.second;
}
template <class T1, class T2>
ostream& operator<<(ostream& os, const pair<T1, T2>& p) {
  return os << p.first << " " << p.second;
}
template <class T>
istream& operator>>(istream& is, vector<T>& a) {
  for (auto& v : a) is >> v;
  return is;
}
template <class T>
ostream& operator<<(ostream& os, const vector<T>& a) {
  for (auto it = a.begin(); it != a.end();) {
    os << *it;
    if (++it != a.end()) os << " ";
  }
  return os;
}
template <class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N>& a) {
  for (auto it = a.begin(); it != a.end();) {
    os << *it;
    if (++it != a.end()) os << " ";
  }
  return os;
}
template <class T>
ostream& operator<<(ostream& os, const set<T>& st) {
  os << "{";
  for (auto it = st.begin(); it != st.end();) {
    os << *it;
    if (++it != st.end()) os << ",";
  }
  os << "}";
  return os;
}
template <class T1, class T2>
ostream& operator<<(ostream& os, const map<T1, T2>& mp) {
  os << "{";
  for (auto it = mp.begin(); it != mp.end();) {
    os << it->first << ":" << it->second;
    if (++it != mp.end()) os << ",";
  }
  os << "}";
  return os;
}

void in() {}
template <typename T, class... U>
void in(T& t, U&... u) {
  cin >> t;
  in(u...);
}
template <class... T>
void in_zip(int n, T&... t) {
  assert(n >= 0 && ((size(t) >= static_cast<size_t>(n)) && ...));
  for (int i = 0; i < n; i++) in(t[i]...);
}
void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T& t, const U&... u) {
  cout << t;
  if (sizeof...(u)) cout << sep;
  out(u...);
}
template <class T, class U>
void out_opt(const optional<T>& opt, const U& fallback, ostream& os = cout) {
  if (opt.has_value())
    os << opt.value();
  else
    os << fallback;
  os << "\n";
}
template <class T, class U>
void out_opt(const vector<optional<T>>& vec, const U& fallback, ostream& os = cout) {
  for (auto it = vec.begin(); it != vec.end();) {
    if ((*it).has_value())
      os << (*it).value();
    else
      os << fallback;
    if (++it != vec.end()) os << " ";
  }
  os << "\n";
}

namespace IO {
template <class T, class... U>
T read(U&&... u) {
  T t = T(forward<U>(u)...);
  in(t);
  return t;
}
namespace Graph {
vector<vector<int>> unweighted(int n, int m, bool directed = false, int offset = 1) {
  vector<vector<int>> g(n);
  for (int i = 0; i < m; i++) {
    int u, v;
    cin >> u >> v;
    u -= offset, v -= offset;
    g[u].push_back(v);
    if (!directed) g[v].push_back(u);
  }
  return g;
}
template <class T>
vector<vector<pair<int, T>>> weighted(int n, int m, bool directed = false, int offset = 1) {
  vector<vector<pair<int, T>>> g(n);
  for (int i = 0; i < m; i++) {
    int u, v;
    T w;
    cin >> u >> v >> w;
    u -= offset, v -= offset;
    g[u].push_back({v, w});
    if (!directed) g[v].push_back({u, w});
  }
  return g;
}
}  // namespace Graph
namespace Tree {
vector<vector<int>> unweighted(int n, bool directed = false, int offset = 1) {
  return Graph::unweighted(n, n - 1, directed, offset);
}
template <class T>
vector<vector<pair<int, T>>> weighted(int n, bool directed = false, int offset = 1) {
  return Graph::weighted<T>(n, n - 1, directed, offset);
}
vector<vector<int>> rooted(int n, bool to_root = true, bool to_leaf = true, int offset = 1) {
  vector<vector<int>> g(n);
  for (int i = 1; i < n; i++) {
    int p;
    cin >> p;
    p -= offset;
    if (to_root) g[i].push_back(p);
    if (to_leaf) g[p].push_back(i);
  }
  return g;
}
}  // namespace Tree
}  // namespace IO
#line 10 "template/template.hpp"

#line 2 "template/debug.hpp"
#ifdef LOCAL
#define debug 1
#define show(...) _show(0, #__VA_ARGS__, __VA_ARGS__)
#else
#define debug 0
#define show(...) true
#endif
template <class T>
void _show(int, T) {
  cerr << '\n';
}
template <class T1, class T2, class... T3>
void _show(int i, const T1& a, const T2& b, const T3&... c) {
  for (; a[i] != ',' && a[i] != '\0'; i++) cerr << a[i];
  cerr << ":" << b << " ";
  _show(i + 1, a, c...);
}
#line 2 "modint/binomial-general-mod.hpp"

#line 2 "math/barrett.hpp"

struct barrett {
  unsigned int _m;
  unsigned long long im;
  explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
  unsigned int umod() const { return _m; }
  unsigned int mul(unsigned int a, unsigned int b) const {
    unsigned long long z = a;
    z *= b;
#ifdef _MSC_VER
    unsigned long long x;
    _umul128(z, im, &x);
#else
    unsigned long long x = (unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
    unsigned long long y = x * _m;
    return (unsigned int)(z - y + (z < y ? _m : 0));
  }
};
#line 4 "modint/binomial-general-mod.hpp"

struct BinomialGeneralMod {
  using u32 = unsigned int;
  using u64 = unsigned long long;
  BinomialGeneralMod() : m(1) {}
  BinomialGeneralMod(u32 mod) : m(mod) {
    u32 m1 = m;
    for (u32 p = 2; (u64)p * p <= m1; p += (p & 1) + 1) {
      if (m1 % p == 0) add_prime_power(p, m1);
    }
    if (m1 > 1) add_prime_power(m1, m1);
    u32 crt_mod = 1;
    for (u32 q : qs) {
      crt_inv.push_back(inv_mod(crt_mod % q, q));
      crt_mod *= q;
    }
  }
  u32 get_mod() const { return m; }
  u32 binom(u64 n, u64 k) const {
    if (n < k) return 0;
    u32 val = 0, mod = 1;
    for (u32 i = 0; i < ps.size(); i++) {
      u32 p = ps[i], e = es[i], q = qs[i];
      auto& f = fs[i];
      auto& fi = fis[i];
      const barrett& bt = brs[i];
      u32 val1 = 1;
      u64 e1 = 0;
      for (u64 x = n; x;) {
        val1 = bt.mul(bt.mul(val1, f[x % q]), block_pow(bt, f[q - 1], x / q));
        e1 += x /= p;
      }
      for (u64 x = k; x;) {
        val1 = bt.mul(bt.mul(val1, fi[x % q]), block_pow(bt, fi[q - 1], x / q));
        e1 -= x /= p;
      }
      for (u64 x = n - k; x;) {
        val1 = bt.mul(bt.mul(val1, fi[x % q]), block_pow(bt, fi[q - 1], x / q));
        e1 -= x /= p;
      }
      val1 = e1 >= e ? 0 : bt.mul(val1, pow(bt, p, e1));
      val += (u64)bt.mul(val1 + q - val % q, crt_inv[i]) * mod;
      mod *= q;
    }
    return val;
  }

 private:
  const u32 m;
  vector<u32> ps, es, qs, crt_inv;
  vector<barrett> brs;
  vector<vector<u32>> fs, fis;
  void add_prime_power(u32 p, u32& m1) {
    u32 e = 0, q = 1;
    while (m1 % p == 0) m1 /= p, e++, q *= p;
    barrett bt(q);
    ps.push_back(p);
    es.push_back(e);
    qs.push_back(q);
    brs.push_back(bt);
    vector<u32> f(q, 1), fi(q, 1);
    for (u32 i = 1; i < q; i++) f[i] = i % p == 0 ? f[i - 1] : bt.mul(f[i - 1], i);
    fs.push_back(f);
    fi[q - 1] = inv_mod(f[q - 1], q);
    for (u32 i = q - 1; i > 0; i--) fi[i - 1] = i % p == 0 ? fi[i] : bt.mul(fi[i], i);
    fis.push_back(fi);
  }
  u32 block_pow(const barrett& bt, u32 x, u64 n) const {
    u32 mod = bt.umod();
    if (x == 1 || mod == 1) return 1 % mod;
    if (x + 1 == mod) return n % 2 ? x : 1;
    return pow(bt, x, n);
  }
  u32 pow(const barrett& bt, u32 x, u64 n) const {
    u32 y = 1;
    while (n) {
      if (n & 1) y = bt.mul(x, y);
      x = bt.mul(x, x);
      n >>= 1;
    }
    return y;
  }
  u32 inv_mod(u32 a, u32 mod) const {
    long long x = a, y = mod;
    long long u = 1, v = 0;
    while (y) {
      long long t = x / y;
      swap(x -= t * y, y);
      swap(u -= t * v, v);
    }
    if (u < 0) u += mod;
    return u;
  }
};

/**
 * @brief 一般 mod での二項係数
 * @docs docs/modint/binomial-general-mod.md
 */
#line 5 "verify/modint/LC_binomial_coefficient.test.cpp"

int main() {
  int t, m;
  in(t, m);
  BinomialGeneralMod binom(m);
  while (t--) {
    ll n, k;
    in(n, k);
    out(binom.binom(n, k));
  }
}

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