結果

問題 No.1050 Zero (Maximum)
コンテスト
ユーザー kya_ski
提出日時 2020-05-21 23:25:38
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 25 ms / 2,000 ms
コード長 4,413 bytes
コンパイル時間 1,853 ms
コンパイル使用メモリ 174,168 KB
実行使用メモリ 6,820 KB
最終ジャッジ日時 2024-10-02 09:14:35
合計ジャッジ時間 2,543 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge5
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ファイルパターン 結果
sample AC * 3
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>
using namespace std;

template<int mod> struct ModInt {
    int x;
    ModInt() : x(0) {}
    ModInt(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
    ModInt &operator+=(const ModInt &p) { if((x += p.x) >= mod) x -= mod; return *this; }
    ModInt &operator-=(const ModInt &p) { if((x += mod-p.x) >= mod) x -= mod; return *this; }
    ModInt &operator*=(const ModInt &p) { x = (int)(1LL*x*p.x%mod); return *this; }
    ModInt &operator/=(const ModInt &p) { *this *= p.inverse(); return *this; }
    ModInt operator-() const { return ModInt(-x); }
    ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
    ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
    ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
    ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
    bool operator==(const ModInt &p) const { return x == p.x; }
    bool operator!=(const ModInt &p) const { return x != p.x; }
    ModInt inverse() const {
        int a = x, b = mod, u = 1, v = 0, t;
        while(b > 0) { t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); }
        return ModInt(u);
    }
    ModInt pow(long long e){
        long long a = 1, p = x;
        while(e > 0) {
            if (e & 1) {a = (a * p) % mod; e--;}
            else {p = (p * p) % mod; e /= 2;}
        }
        return ModInt(a);
    }
    friend ostream &operator<<(ostream &os, const ModInt<mod> &p) {
        return os << p.x;
    }
    friend istream &operator>>(istream &is, ModInt<mod> &a) {
        long long x;
        is >> x;
        a = ModInt<mod>(x);
        return (is);
    }
};


template<class T> struct Matrix {
private :
    vector<vector<T>> A;
public :
    Matrix () { }

    Matrix (size_t n, size_t m) : A(n, vector<T>(m, 0)) { }

    Matrix (size_t n) : A(n, vector<T>(n, 0)) { };

    Matrix (const vector<vector<T>> &B) { A = B; }

    size_t height() const { return (A.size()); }

    size_t width() const { return (A[0].size()); }

    inline const vector<T> &operator[] (int k) const {
        return (A.at(k));
    }

    inline vector<T> &operator[] (int k) {
        return (A.at(k));
    }

    static Matrix E(size_t n) {
        Matrix mat(n);
        for (int i = 0; i < n; i++) mat[i][i] = 1;
        return (mat);
    }

    Matrix &operator+= (const Matrix &B) {
        size_t n = height(), m = width();
        assert(n == B.height() and m == B.width());
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                (*this)[i][j] += B[i][j];
            }
        }
        return (*this);
    }

    Matrix &operator-= (const Matrix &B) {
        size_t n = height(), m = width();
        assert(n == B.height() and m == B.width());
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                (*this)[i][j] -= B[i][j];
            }
        }
        return (*this);
    }

    Matrix &operator*= (const Matrix &B) {
        size_t n = height(), m = B.width(), p = width();
        assert(p == B.height());
        vector<vector<T>> C(n, vector<T>(m, 0));
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                for (int k = 0; k < p; k++) {
                    C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]);
                }
            }
        }
        A.swap(C);
        return (*this);
    }

    Matrix &operator^= (long long k) {
        Matrix B = Matrix::E(height());
        while (k > 0) {
            if (k&1) B *= (*this);
            (*this) *= (*this);
            k >>= 1LL;
        }
        A.swap(B.A);
        return (*this);
    }

    Matrix operator+ (const Matrix &B) const {
        return (Matrix(*this) += B);
    }

    Matrix operator- (const Matrix &B) const {
        return (Matrix(*this) -= B);
    }

    Matrix operator* (const Matrix &B) const {
        return (Matrix(*this) *= B);
    }

    Matrix operator^ (const long long k) const {
        return (Matrix(*this) ^= k);
    }

};

constexpr int MOD = 1'000'000'007;

int main() {
    int m, k;
    cin >> m >> k;
    Matrix<ModInt<MOD>> dp(m);
    for (int i = 0; i < m; i++) {
        for (int j = 0; j < m; j++) {
            dp[i][(i + j) % m] += 1;
            dp[i][(i * j) % m] += 1;
        }
    }

    dp ^= k;
    
    cout << dp[0][0] << '\n';

    return 0;
}
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