#535035 (C++17) No.1181 Product Sum for All Subsets

• 問題: No.1181 Product Sum for All Subsets
• ユーザー: Haar
• 提出日時: 2020-08-21 22:09:10
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 41 ms / 2,000 ms
• コード長: 4,569 bytes
• コンパイル時間: 2,132 ms
• コンパイル使用メモリ: 206,560 KB
• 実行使用メモリ: 5,248 KB
• 最終ジャッジ日時: 2024-10-15 05:41:55
• 合計ジャッジ時間: 3,584 ms
• ジャッジサーバーID （参考情報）: judge3 / judge5

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 5,248 KB
testcase_01	AC	2 ms; 5,248 KB
testcase_02	AC	3 ms; 5,248 KB
testcase_03	AC	2 ms; 5,248 KB
testcase_04	AC	2 ms; 5,248 KB
testcase_05	AC	2 ms; 5,248 KB
testcase_06	AC	2 ms; 5,248 KB
testcase_07	AC	2 ms; 5,248 KB
testcase_08	AC	2 ms; 5,248 KB
testcase_09	AC	2 ms; 5,248 KB
testcase_10	AC	2 ms; 5,248 KB
testcase_11	AC	2 ms; 5,248 KB
testcase_12	AC	35 ms; 5,248 KB
testcase_13	AC	8 ms; 5,248 KB
testcase_14	AC	33 ms; 5,248 KB
testcase_15	AC	26 ms; 5,248 KB
testcase_16	AC	36 ms; 5,248 KB
testcase_17	AC	16 ms; 5,248 KB
testcase_18	AC	31 ms; 5,248 KB
testcase_19	AC	28 ms; 5,248 KB
testcase_20	AC	35 ms; 5,248 KB
testcase_21	AC	19 ms; 5,248 KB
testcase_22	AC	12 ms; 5,248 KB
testcase_23	AC	5 ms; 5,248 KB
testcase_24	AC	10 ms; 5,248 KB
testcase_25	AC	18 ms; 5,248 KB
testcase_26	AC	3 ms; 5,248 KB
testcase_27	AC	2 ms; 5,248 KB
testcase_28	AC	41 ms; 5,248 KB
testcase_29	AC	41 ms; 5,248 KB

ソースコード

#include <bits/stdc++.h>

/**
 * @title Modint
 * @docs mint.md
 */
template <int32_t M> class ModInt{
public:
  constexpr static int32_t MOD = M;
  uint32_t val;
  
  constexpr ModInt(): val(0){}
  constexpr ModInt(int64_t n){
    if(n >= M) val = n % M;
    else if(n < 0) val = n % M + M;
    else val = n;
  }
  
  constexpr auto& operator=(const ModInt &a){val = a.val; return *this;}
  constexpr auto& operator+=(const ModInt &a){
    if(val + a.val >= M) val = (uint64_t)val + a.val - M;
    else val += a.val;
    return *this;
  }
  constexpr auto& operator-=(const ModInt &a){
    if(val < a.val) val += M;
    val -= a.val;
    return *this;
  }
  constexpr auto& operator*=(const ModInt &a){
    val = (uint64_t)val * a.val % M;
    return *this;
  }
  constexpr auto& operator/=(const ModInt &a){
    val = (uint64_t)val * a.inv().val % M;
    return *this;
  }

  constexpr auto operator+(const ModInt &a) const {return ModInt(*this) += a;}
  constexpr auto operator-(const ModInt &a) const {return ModInt(*this) -= a;}
  constexpr auto operator*(const ModInt &a) const {return ModInt(*this) *= a;}
  constexpr auto operator/(const ModInt &a) const {return ModInt(*this) /= a;}
  
  constexpr bool operator==(const ModInt &a) const {return val == a.val;}
  constexpr bool operator!=(const ModInt &a) const {return val != a.val;}
  
  constexpr auto& operator++(){*this += 1; return *this;}
  constexpr auto& operator--(){*this -= 1; return *this;}
  
  constexpr auto operator++(int){auto t = *this; *this += 1; return t;}
  constexpr auto operator--(int){auto t = *this; *this -= 1; return t;}
  
  constexpr static ModInt power(int64_t n, int64_t p){
    if(p < 0) return power(n, -p).inv();
    
    int64_t ret = 1, e = n % M;
    for(; p; (e *= e) %= M, p >>= 1) if(p & 1) (ret *= e) %= M;
    return ret;
  }
  
  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;
  }
  
  constexpr static auto frac(int64_t a, int64_t b){return ModInt(a) / ModInt(b);}
  
  constexpr auto power(int64_t p) const {return power(val, p);}
  constexpr auto inv() const {return inv(val);}
  
  friend constexpr auto operator-(const ModInt &a){return ModInt(M-a.val);}
  
  friend constexpr auto operator+(int64_t a, const ModInt &b){return ModInt(a) + b;}
  friend constexpr auto operator-(int64_t a, const ModInt &b){return ModInt(a) - b;}
  friend constexpr auto operator*(int64_t a, const ModInt &b){return ModInt(a) * b;}
  friend 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>
  static auto div(){
    static auto value = inv(N);
    return value;
  }

  explicit operator int32_t() const noexcept {return val;}
  explicit operator int64_t() const noexcept {return val;}
};

/**
 * @title Factorial table
 * @docs factorial_table.md
 */
template <typename T> class FactorialTable{
  using value_type = T;
  
  std::vector<T> f_table;
  std::vector<T> if_table;

public:
  FactorialTable(int N){
    f_table.assign(N+1, 1);
    if_table.assign(N+1, 1);
    
    for(int i = 1; i <= N; ++i){
      f_table[i] = f_table[i-1] * i;
    }
    
    if_table[N] = f_table[N].inv();

    for(int i = N-1; i >= 0; --i){
      if_table[i] = if_table[i+1] * (i+1);
    }
  }
  
  T factorial(int64_t i) const {
    assert(i < (int)f_table.size());
    return f_table[i];
  }
  
  T inv_factorial(int64_t i) const {
    assert(i < (int)if_table.size());
    return if_table[i];
  }

  T P(int64_t n, int64_t k) const {
    if(n < k or n < 0 or k < 0) return 0;
    return factorial(n) * inv_factorial(n-k);
  }

  T C(int64_t n, int64_t k) const {
    if(n < k or n < 0 or k < 0) return 0;
    return P(n,k) * inv_factorial(k);
  }

  T H(int64_t n, int64_t k) const {
    if(n == 0 and k == 0) return 1;
    return C(n+k-1, k);
  }
};



namespace solver{
  using mint = ModInt<1000000007>;
  
  void solve(){
    int64_t N, K; std::cin >> N >> K;
    auto ft = FactorialTable<mint>(N);

    mint ans = 0;

    mint s = mint(K) * mint(K + 1) / mint(2);

    for(int i = 0; i < N; ++i){
      ans += ft.C(N, i) * mint::power(K, N - i) * s.power(i);
    }

    

    std::cout << ans << "\n";
  }
}

int main(){
  solver::solve();
  return 0;
}