結果

問題 No.1044 正直者大学
ユーザー HaarHaar
提出日時 2020-05-01 22:34:53
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 32 ms / 2,000 ms
コード長 4,846 bytes
コンパイル時間 2,132 ms
コンパイル使用メモリ 204,804 KB
実行使用メモリ 9,636 KB
最終ジャッジ日時 2024-06-07 10:55:28
合計ジャッジ時間 3,536 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge1
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 10 ms
9,564 KB
testcase_01 AC 10 ms
9,448 KB
testcase_02 AC 9 ms
9,500 KB
testcase_03 AC 10 ms
9,552 KB
testcase_04 AC 9 ms
9,552 KB
testcase_05 AC 10 ms
9,416 KB
testcase_06 AC 32 ms
9,604 KB
testcase_07 AC 10 ms
9,460 KB
testcase_08 AC 10 ms
9,596 KB
testcase_09 AC 11 ms
9,480 KB
testcase_10 AC 10 ms
9,516 KB
testcase_11 AC 10 ms
9,516 KB
testcase_12 AC 11 ms
9,556 KB
testcase_13 AC 21 ms
9,460 KB
testcase_14 AC 10 ms
9,616 KB
testcase_15 AC 11 ms
9,620 KB
testcase_16 AC 24 ms
9,408 KB
testcase_17 AC 19 ms
9,608 KB
testcase_18 AC 20 ms
9,516 KB
testcase_19 AC 16 ms
9,508 KB
testcase_20 AC 13 ms
9,636 KB
testcase_21 AC 14 ms
9,444 KB
testcase_22 AC 10 ms
9,592 KB
testcase_23 AC 10 ms
9,520 KB
testcase_24 AC 11 ms
9,500 KB
testcase_25 AC 10 ms
9,572 KB
testcase_26 AC 10 ms
9,480 KB
testcase_27 AC 10 ms
9,508 KB
testcase_28 AC 10 ms
9,520 KB
testcase_29 AC 10 ms
9,500 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <bits/stdc++.h>

template <uint32_t M> class ModInt{
public:
  uint64_t val;
  
  constexpr ModInt(): val(0){}
  constexpr ModInt(std::int64_t n){
    if(n >= M) val = n % M;
    else if(n < 0) val = n % M + M;
    else val = n;
  }
  
  inline constexpr auto operator+(const ModInt &a) const {return ModInt(val + a.val);}
  inline constexpr auto operator-(const ModInt &a) const {return ModInt(val - a.val);}
  inline constexpr auto operator*(const ModInt &a) const {return ModInt(val * a.val);}
  inline constexpr auto operator/(const ModInt &a) const {return ModInt(val * a.inv().val);}
  
  inline constexpr auto& operator=(const ModInt &a){val = a.val; return *this;}
  inline constexpr auto& operator+=(const ModInt &a){if((val += a.val) >= M) val -= M; return *this;}
  inline constexpr auto& operator-=(const ModInt &a){if(val < a.val) val += M; val -= a.val; return *this;}
  inline constexpr auto& operator*=(const ModInt &a){(val *= a.val) %= M; return *this;}
  inline constexpr auto& operator/=(const ModInt &a){(val *= a.inv().val) %= M; return *this;}
 
  inline constexpr bool operator==(const ModInt &a) const {return val == a.val;}
  inline constexpr bool operator!=(const ModInt &a) const {return val != a.val;}
 
  inline constexpr auto& operator++(){*this += 1; return *this;}
  inline constexpr auto& operator--(){*this -= 1; return *this;}
 
  inline constexpr auto operator++(int){auto t = *this; *this += 1; return t;}
  inline constexpr auto operator--(int){auto t = *this; *this -= 1; return t;}
 
  inline constexpr static ModInt power(int64_t n, int64_t p){
    if(p < 0) return power(n, -p).inv();
    
    int64_t ret = 1, e = n;
    for(; p; (e *= e) %= M, p >>= 1) if(p & 1) (ret *= e) %= M;
    return ret;
  }
 
  inline constexpr static ModInt inv(int64_t a){
    int64_t b = M, u = 1, v = 0;
    
    while(b){
      int64_t t = a / b;
      a -= t * b; std::swap(a,b);
      u -= t * v; std::swap(u,v);
    }
 
    u %= M;
    if(u < 0) u += M;
    
    return u;
  }
 
  inline constexpr static auto frac(int64_t a, int64_t b){return ModInt(a) / ModInt(b);}
  
  inline constexpr auto power(int64_t p) const {return power(val, p);}
  inline constexpr auto inv() const {return inv(val);}
 
  friend inline constexpr auto operator-(const ModInt &a){return ModInt(-a.val);}
 
  friend inline constexpr auto operator+(int64_t a, const ModInt &b){return ModInt(a) + b;}
  friend inline constexpr auto operator-(int64_t a, const ModInt &b){return ModInt(a) - b;}
  friend inline constexpr auto operator*(int64_t a, const ModInt &b){return ModInt(a) * b;}
  friend inline constexpr auto operator/(int64_t a, const ModInt &b){return ModInt(a) / b;}
 
  friend std::istream& operator>>(std::istream &s, ModInt<M> &a){s >> a.val; return s;}
  friend std::ostream& operator<<(std::ostream &s, const ModInt<M> &a){s << a.val; return s;}

  template <int N>
  inline static auto div(){
    static auto value = inv(N);
    return value;
  }
};


/**
 * @attention 使用前にinit関数を呼び出す
 */
template <typename T> class Combinatorics{
public:
  static std::vector<T> facto;
  static std::vector<T> ifacto;

  static void init(int N){
    facto.assign(N+1, 1);
    ifacto.assign(N+1, 1);

    for(int i = 1; i <= N; ++i){
      facto[i] = facto[i-1] * i;
    }

    ifacto[N] = facto[N].inv();

    for(int i = N-1; i >= 0; --i){
      ifacto[i] = ifacto[i+1] * (i+1);
    }
  }

  static T f(int64_t i){
    assert(i < facto.size());
    return facto[i];
  }
  
  static T finv(int64_t i){
    assert(i < ifacto.size());
    return ifacto[i];
  }

  static T P(int64_t n, int64_t k);
  static T C(int64_t n, int64_t k);
  static T H(int64_t n, int64_t k);
  static T stirling_number(int64_t n, int64_t k);
  static T bell_number(int64_t n, int64_t k);
  static std::vector<T> bernoulli_number(int64_t n);
  static T catalan_number(int64_t n);
};

template <typename T> std::vector<T> Combinatorics<T>::facto = std::vector<T>();
template <typename T> std::vector<T> Combinatorics<T>::ifacto = std::vector<T>();

template <typename T> T Combinatorics<T>::P(int64_t n, int64_t k){
  if(n < k or n < 0 or k < 0) return 0;
  return f(n) * finv(n-k);
}

template <typename T> T Combinatorics<T>::C(int64_t n, int64_t k){
  if(n < k or n < 0 or k < 0) return 0;
  return P(n,k) * finv(k);
}

template <typename T> T Combinatorics<T>::H(int64_t n, int64_t k){
  if(n == 0 and k == 0) return 1;
  return C(n+k-1, k);
}





using mint = ModInt<1000000007>;
using C = Combinatorics<mint>;

int main(){
  C::init(400000);
  
  int N, M, K; std::cin >> N >> M >> K;

  mint ans = 0;

  for(int i = 1; i <= N + M; ++i){
    if(N + M - 2 * i >= K){
      mint t = 0;
      t += C::C(N-1, i-1) * C::f(N) * C::C(M-1, i-1) * C::f(M) / i;
      ans += t;
    }
  }
  
  std::cout << ans << std::endl;

  return 0;
}
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