math/comb-modP.hpp

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• Last update: 2023-03-13 14:46:41+09:00
• Include: #include "math/comb-modP.hpp"

Depends on

• math/mint.hpp

Code

#include "mint.hpp"

constexpr int len = 2000010;
constexpr int f_size = min(len, mod);
mint fact[f_size], invfact[f_size], inv[f_size];
struct initializer {
  initializer(){
    fact[0] = fact[1] = inv[1] = 1;
    invfact[0] = invfact[1] = 1;
    for(int i = 2; i < f_size; i++){
      fact[i] = fact[i - 1] * i;
      inv[i] = -inv[mod % i] * (mod/i);
      invfact[i] = invfact[i - 1] * inv[i];
    }
  }
} initializer;
mint C(int n, int r){
  assert(0 <= n && n < len);
  mint res = 1;
  while(r){
    int a = n % mod;
    int b = r % mod;
    if(a < b) return 0;
    res *= fact[a] * invfact[b] * invfact[a - b];
    n /= mod;
    r /= mod;
  }
  return res;
}
mint H(int n, int r){
  assert(0 < n && 0 <= r);
  assert(0 < n+r && n+r <= len);
  return C(n + r - 1, r);
}

#line 2 "math/mint.hpp"

template <int mod>
struct Mint {
  ll x;
  constexpr Mint(ll x = 0) : x((x + mod) % mod){}
  static constexpr int get_mod(){ return mod; }
  constexpr Mint operator-() const{ return Mint(-x); }
  constexpr Mint operator+=(const Mint &a){
    if((x += a.x) >= mod) x -= mod;
    return *this;
  }
  constexpr Mint &operator++(){
    if(++x == mod) x = 0;
    return *this;
  }
  constexpr Mint operator++(int){
    Mint temp = *this;
    if(++x == mod) x = 0;
    return temp;
  }
  constexpr Mint &operator-=(const Mint &a){
    if((x -= a.x) < 0) x += mod;
    return *this;
  }
  constexpr Mint &operator--(){
    if(--x < 0) x += mod;
    return *this;
  }
  constexpr Mint operator--(int){
    Mint temp = *this;
    if(--x < 0) x += mod;
    return temp;
  }
  constexpr Mint &operator*=(const Mint &a){
    (x *= a.x) %= mod;
    return *this;
  }
  constexpr Mint operator+(const Mint &a) const{ return Mint(*this) += a; }
  constexpr Mint operator-(const Mint &a) const{ return Mint(*this) -= a; }
  constexpr Mint operator*(const Mint &a) const{ return Mint(*this) *= a; }
  constexpr Mint pow(ll t) const{
    if(!t) return 1;
    Mint res = 1, v = *this;
    while(t){
      if(t & 1) res *= v;
      v *= v;
      t >>= 1;
    }
    return res;
  }
  constexpr Mint inv() const{ return pow(mod - 2); }
  constexpr Mint &operator/=(const Mint &a){ return (*this) *= a.inv(); }
  constexpr Mint operator/(const Mint &a) const{ return Mint(*this) /= a; }
  constexpr bool operator==(const Mint &a) const{ return x == a.x; }
  constexpr bool operator!=(const Mint &a) const{ return x != a.x; }
  constexpr bool operator<(const Mint &a) const{ return x < a.x; }
  constexpr bool operator>(const Mint &a) const{ return x > a.x; }
  friend istream &operator>>(istream &is, Mint &a){ return is >> a.x; }
  friend ostream &operator<<(ostream &os, const Mint &a){ return os << a.x; }
};
//using mint = Mint<1000000007>;
#line 2 "math/comb-modP.hpp"

constexpr int len = 2000010;
constexpr int f_size = min(len, mod);
mint fact[f_size], invfact[f_size], inv[f_size];
struct initializer {
  initializer(){
    fact[0] = fact[1] = inv[1] = 1;
    invfact[0] = invfact[1] = 1;
    for(int i = 2; i < f_size; i++){
      fact[i] = fact[i - 1] * i;
      inv[i] = -inv[mod % i] * (mod/i);
      invfact[i] = invfact[i - 1] * inv[i];
    }
  }
} initializer;
mint C(int n, int r){
  assert(0 <= n && n < len);
  mint res = 1;
  while(r){
    int a = n % mod;
    int b = r % mod;
    if(a < b) return 0;
    res *= fact[a] * invfact[b] * invfact[a - b];
    n /= mod;
    r /= mod;
  }
  return res;
}
mint H(int n, int r){
  assert(0 < n && 0 <= r);
  assert(0 < n+r && n+r <= len);
  return C(n + r - 1, r);
}

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