結果

問題 No.1102 Remnants
コンテスト
ユーザー Haar
提出日時 2020-07-04 09:10:45
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 896 ms / 2,000 ms
コード長 4,400 bytes
コンパイル時間 1,908 ms
コンパイル使用メモリ 199,156 KB
最終ジャッジ日時 2025-01-11 15:27:12
ジャッジサーバーID
（参考情報） 		judge4 / judge5
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ファイルパターン 結果
sample AC * 3
other AC * 25
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>

#ifdef DEBUG
#include <Mylib/Debug/debug.cpp>
#else
#define dump(...)
#endif

/**
 * @title Modint
 * @docs mint.md
 */
template <uint32_t M> class ModInt{
public:
  constexpr static uint32_t MOD = M;
  uint64_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;
  }
  
  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 % M;
    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;
  }

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

using mint = ModInt<1000000007>;

template <typename T>
struct BigCombination{
  T kfinv;
  std::vector<T> f, finv;
  int l;
  
  BigCombination(int K, int l, int r): l(l){
    const int len = r - l + 1;

    kfinv = 1;
    for(int i = 1; i <= K; ++i) kfinv *= i;
    kfinv = kfinv.inv();

    f.resize(len);
    finv.resize(len);

    f[0] = 1;
    for(int i = 1; i <= l; ++i) f[0] *= i;
    for(int i = l + 1; i <= r; ++i) f[i - l] = f[i - l - 1] * i;

    finv.back() = 1;
    for(int i = 1; i <= r - K; ++i) finv.back() *= i;
    finv.back() = finv.back().inv();

    for(int i = r - K - 1; i >= l - K; --i) finv[i - (l - K)] = finv[i - (l - K) + 1] * (i + 1);
  }

  T operator[](int n) const {return kfinv * f[n - l] * finv[n - l];}
};


int main(){
  std::cin.tie(0);
  std::ios::sync_with_stdio(false);
  
  int N, K;

  while(std::cin >> N >> K){
    std::vector<int> A(N);
    for(int i = 0; i < N; ++i) std::cin >> A[i];

    BigCombination<mint> bc(K, K, K + N);

    mint ans = 0;

    for(int i = 0; i < N; ++i){
      ans += bc[K + i] * bc[K + N - i - 1] * A[i];
    }

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

  return 0;
}
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