結果

問題 No.665 Bernoulli Bernoulli
コンテスト
ユーザー Haar
提出日時 2019-08-10 07:31:29
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 413 ms / 2,000 ms
コード長 5,819 bytes
コンパイル時間 2,275 ms
コンパイル使用メモリ 197,980 KB
最終ジャッジ日時 2025-01-07 11:38:07
ジャッジサーバーID
（参考情報） 		judge4 / judge3
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 4
other AC * 15
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>
#define LLI long long int
#define FOR(v, a, b) for(LLI v = (a); v < (b); ++v)
#define FORE(v, a, b) for(LLI v = (a); v <= (b); ++v)
#define REP(v, n) FOR(v, 0, n)
#define REPE(v, n) FORE(v, 0, n)
#define REV(v, a, b) for(LLI v = (a); v >= (b); --v)
#define ALL(x) (x).begin(), (x).end()
#define RALL(x) (x).rbegin(), (x).rend()
#define ITR(it, c) for(auto it = (c).begin(); it != (c).end(); ++it)
#define RITR(it, c) for(auto it = (c).rbegin(); it != (c).rend(); ++it)
#define EXIST(c,x) ((c).find(x) != (c).end())
#define fst first
#define snd second
#define popcount __builtin_popcount
#define UNIQ(v) (v).erase(unique(ALL(v)), (v).end())
#define bit(i) (1LL<<(i))

#ifdef DEBUG
#include <misc/C++/Debug.cpp>
#else
#define dump(...) ((void)0)
#endif

#define gcd __gcd

using namespace std;
template <class T> constexpr T lcm(T m, T n){return m/gcd(m,n)*n;}

template <typename I> void join(ostream &ost, I s, I t, string d=" "){for(auto i=s; i!=t; ++i){if(i!=s)ost<<d; ost<<*i;}ost<<endl;}
template <typename T> istream& operator>>(istream &is, vector<T> &v){for(auto &a : v) is >> a; return is;}

template <typename T, typename U> bool chmin(T &a, const U &b){return (a>b ? a=b, true : false);}
template <typename T, typename U> bool chmax(T &a, const U &b){return (a<b ? a=b, true : false);}
template <typename T, size_t N, typename U> void fill_array(T (&a)[N], const U &v){fill((U*)a, (U*)(a+N), v);}

constexpr LLI mod = 1e9+7;


template <uint32_t M> class ModInt{
public:
  uint64_t val;
  ModInt(): val(0){}
  ModInt(int64_t n): val(n>=M ? n%M : n){}
  
  inline constexpr ModInt operator+(const ModInt &a) const {return ModInt((val+a.val)%M);}
  inline constexpr ModInt operator-(const ModInt &a) const {return ModInt((val-a.val+M)%M);}
  inline constexpr ModInt operator*(const ModInt &a) const {return ModInt((val*a.val)%M);}
  inline constexpr ModInt operator/(const ModInt &a) const {return ModInt((val*a.inv().val)%M);}
  
  inline constexpr ModInt& operator=(const ModInt &a){val = a.val; return *this;}
  inline constexpr ModInt& operator+=(const ModInt &a){if((val += a.val) >= M) val -= M; return *this;}
  inline constexpr ModInt& operator-=(const ModInt &a){if(val < a.val) val += M; val -= a.val; return *this;}
  inline constexpr ModInt& operator*=(const ModInt &a){(val *= a.val) %= M; return *this;}
  inline constexpr ModInt& 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 ModInt power(LLI p) const{
    ModInt ret = 1, e = val;
    for(; p; e *= e, p >>= 1) if(p&1) ret *= e;

    return ret;
  }

  inline constexpr static ModInt power(LLI n, LLI p){
    ModInt ret = 1, e = n;
    for(; p; e *= e, p >>= 1) if(p&1) ret *= e;

    return ret;
  }
  
  
  inline constexpr ModInt inv() const{
    int64_t a = val, b = M, u = 1, v = 0;

    while(b){
      int64_t t = a/b;
      a -= t*b; swap(a,b);
      u -= t*v; swap(u,v);
    }
    u %= M;
    if(u < 0) u += M;
    
    return u;
  }
};

template <uint32_t M> ModInt<M> operator+(int64_t a, const ModInt<M> &b){return ModInt<M>(ModInt<M>(a)+b.val);}
template <uint32_t M> ModInt<M> operator-(int64_t a, const ModInt<M> &b){return ModInt<M>(ModInt<M>(a)-b.val);}
template <uint32_t M> ModInt<M> operator*(int64_t a, const ModInt<M> &b){return ModInt<M>(ModInt<M>(a)*b.val);}
template <uint32_t M> ModInt<M> operator/(int64_t a, const ModInt<M> &b){return ModInt<M>(ModInt<M>(a)/b.val);}

template <uint32_t M> ModInt<M> operator-(const ModInt<M> &a){return ModInt<M>(-a.val+M);}

template <uint32_t M> istream& operator>>(istream &is, ModInt<M> &a){is >> a.val; return is;}
template <uint32_t M> ostream& operator<<(ostream &os, const ModInt<M> &a){ os << a.val; return os;}


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

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

    FORE(i,1,N){
      facto[i] = facto[i-1] * i;
    }

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

    REV(i,N-1,0){
      ifacto[i] = ifacto[i+1] * (i+1);
    }
  }

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

  static T P(LLI n, LLI k);
  static T C(LLI n, LLI k);
  static T H(LLI n, LLI k);
  static T stirling_number(LLI n, LLI k);
  static T bell_number(LLI n, LLI k);
  static vector<T> bernoulli_number(LLI n);
};

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

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

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

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

template <typename T> vector<T> CombUtilsMint<T>::bernoulli_number(LLI n){
  vector<T> ret(n+1);

  ret[0] = 1;

  FORE(i,1,n){
    FORE(k,0,i-1){
      ret[i] += C(i+1,k) * ret[k];
    }
    ret[i] /= i+1;
    ret[i] = -ret[i];
  }
  
  return ret;
}


using mint = ModInt<mod>;
using C = CombUtilsMint<mint>;




int main(){
  cin.tie(0);
  ios::sync_with_stdio(false);

  C::init(500000);

  LLI n,k;
  while(cin >> n >> k){
    auto b = C::bernoulli_number(k);


    mint ans = 0;


    REPE(i,k){
      ans += C::C(k+1,i) * b[i] * mint::power(n+1,k+1-i);
    }
    
    ans /= k+1;

    cout << ans << endl;
  }
  
  return 0;
}
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