結果

問題 No.665 Bernoulli Bernoulli
ユーザー rniyarniya
提出日時 2020-03-06 17:00:35
言語 C++14
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 3 ms / 2,000 ms
コード長 3,794 bytes
コンパイル時間 1,635 ms
コンパイル使用メモリ 169,976 KB
実行使用メモリ 4,384 KB
最終ジャッジ日時 2023-08-04 05:50:27
合計ジャッジ時間 2,892 ms
ジャッジサーバーID
(参考情報)
judge15 / judge12
このコードへのチャレンジ(β)

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 1 ms
4,376 KB
testcase_01 AC 1 ms
4,376 KB
testcase_02 AC 3 ms
4,376 KB
testcase_03 AC 3 ms
4,376 KB
testcase_04 AC 3 ms
4,384 KB
testcase_05 AC 3 ms
4,380 KB
testcase_06 AC 2 ms
4,376 KB
testcase_07 AC 3 ms
4,376 KB
testcase_08 AC 3 ms
4,376 KB
testcase_09 AC 3 ms
4,376 KB
testcase_10 AC 3 ms
4,376 KB
testcase_11 AC 3 ms
4,380 KB
testcase_12 AC 3 ms
4,380 KB
testcase_13 AC 3 ms
4,376 KB
testcase_14 AC 3 ms
4,376 KB
testcase_15 AC 3 ms
4,380 KB
testcase_16 AC 3 ms
4,376 KB
testcase_17 AC 3 ms
4,376 KB
testcase_18 AC 3 ms
4,380 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>
using namespace std;
const long long MOD=1e9+7;

template<uint_fast64_t Modulus> class modint{
    using u64=uint_fast64_t;
    public:
    u64 a;
    constexpr modint(const u64 x=0) noexcept:a(((x%Modulus)+Modulus)%Modulus){}
    constexpr u64 &value() noexcept{return a;}
    constexpr const u64 &value() const noexcept{return a;}
    constexpr modint &operator+=(const modint &rhs) noexcept{
        a+=rhs.a;
        if (a>=Modulus) a-=Modulus;
        return *this;
    }
    constexpr modint operator+(const modint &rhs) const noexcept{
        return modint(*this)+=rhs;
    }
    constexpr modint &operator++() noexcept{
        return ++a,*this;
    }
    constexpr modint operator++(int) noexcept{
        modint t=*this; return ++a,t;
    }
    constexpr modint &operator-=(const modint &rhs) noexcept{
        if (a<rhs.a) a+=Modulus;
        a-=rhs.a;
        return *this;
    }
    constexpr modint operator-(const modint &rhs) const noexcept{
        return modint(*this)-=rhs;
    }
    constexpr modint &operator--() noexcept{
        return --a,*this;
    }
    constexpr modint operator--(int) noexcept{
        modint t=*this; return --a,t;
    }
    constexpr modint &operator*=(const modint &rhs) noexcept{
        a=a*rhs.a%Modulus;
        return *this;
    }
    constexpr modint operator*(const modint &rhs) const noexcept{
        return modint(*this)*=rhs;
    }
    constexpr modint &operator/=(modint rhs) noexcept{
        u64 exp=Modulus-2;
        while(exp){
            if (exp&1) *this*=rhs;
            rhs*=rhs; exp>>=1;
        }
        return *this;
    }
    constexpr modint operator/(const modint &rhs) const noexcept{
        return modint(*this)/=rhs;
    }
    constexpr modint operator-() const noexcept{
        return modint(Modulus-a);
    }
    constexpr bool operator==(const modint &rhs) const noexcept{
        return a==rhs.a;
    }
    constexpr bool operator!=(const modint &rhs) const noexcept{
        return a!=rhs.a;
    }
    constexpr bool operator!() const noexcept{return !a;}
    friend constexpr modint pow(modint rhs,long long exp) noexcept{
        modint res{1};
        while(exp){
            if (exp&1) res*=rhs;
            rhs*=rhs; exp>>=1;
        }
        return res;
    }
    template<class T> friend constexpr modint operator+(T x,modint y) noexcept{
        return modint(x)+y;
    }
    template<class T> friend constexpr modint operator-(T x,modint y) noexcept{
        return modint(x)-y;
    }
    template<class T> friend constexpr modint operator*(T x,modint y) noexcept{
        return modint(x)*y;
    }
    template<class T> friend constexpr modint operator/(T x,modint y) noexcept{
        return modint(x)/y;
    }
    friend ostream &operator<<(ostream &s,const modint &rhs) noexcept {
        return s << rhs.a;
    }
    friend istream &operator>>(istream &s,modint &rhs) noexcept {
        u64 a; rhs=modint{(s >> a,a)}; return s;
    }
};

using mint=modint<MOD>;

template<typename M>
M Lagrange_Interpolation(vector<M> y,long long T){
    int n=y.size()-1;
    if (T<=n) return y[T];
    vector<M> dp(n+1,1),pd(n+1,1),fac(n+1,1),finv(n+1,1);
    for (int i=0;i<n;++i) dp[i+1]=dp[i]*(T-i);
    for (int i=n;i>0;--i) pd[i-1]=pd[i]*(T-i);
    for (int i=1;i<n+1;++i) fac[i]=fac[i-1]*i;
    finv[n]=M(1)/fac[n];
    for (int i=n;i>0;--i) finv[i-1]=finv[i]*i;
    M res=0;
    for (int i=0;i<=n;++i){
        M x=y[i]*dp[i]*pd[i]*finv[i]*finv[n-i];
        if ((n-i)&1) res-=x;
        else res+=x;
    }
    return res;
}

int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    long long n,k; cin >> n >> k;
    vector<mint> A(k+2,0);
    for (int i=1;i<k+2;++i) A[i]=A[i-1]+pow((mint)i,k);
    mint ans=Lagrange_Interpolation(A,n);
    cout << ans << '\n';
}
0