結果

問題 No.1050 Zero (Maximum)
コンテスト
ユーザー yukinon0808
提出日時 2020-05-08 22:13:11
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 35 ms / 2,000 ms
コード長 7,478 bytes
コンパイル時間 1,841 ms
コンパイル使用メモリ 178,576 KB
実行使用メモリ 6,944 KB
最終ジャッジ日時 2024-07-04 00:49:01
合計ジャッジ時間 2,699 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge2
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 * 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 #
raw source code 

#include <bits/stdc++.h>

using namespace std;

#define REP(i, n) for (int i=0; i<(n); ++i)
#define RREP(i, n) for (int i=(int)(n)-1; i>=0; --i)
#define FOR(i, a, n) for (int i=(a); i<(n); ++i)
#define RFOR(i, a, n) for (int i=(int)(n)-1; i>=(a); --i)

#define SZ(x) ((int)(x).size())
#define ALL(x) (x).begin(),(x).end()

#define DUMP(x) cerr<<#x<<" = "<<(x)<<endl
#define DEBUG(x) cerr<<#x<<" = "<<(x)<<" (L"<<__LINE__<<")"<<endl;

template<class T>
ostream &operator<<(ostream &os, const vector <T> &v) {
    os << "[";
    REP(i, SZ(v)) {
        if (i) os << ", ";
        os << v[i];
    }
    return os << "]";
}

template<class T, class U>
ostream &operator<<(ostream &os, const pair <T, U> &p) {
    return os << "(" << p.first << " " << p.second << ")";
}

template<class T>
bool chmax(T &a, const T &b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}

template<class T>
bool chmin(T &a, const T &b) {
    if (b < a) {
        a = b;
        return true;
    }
    return false;
}

using ll = long long;
using ull = unsigned long long;
using ld = long double;
using P = pair<int, int>;
using vi = vector<int>;
using vll = vector<ll>;
using vvi = vector<vi>;
using vvll = vector<vll>;

const ll MOD = 1e9 + 7;
const int INF = INT_MAX / 2;
const ll LINF = LLONG_MAX / 2;
const ld eps = 1e-9;

template<int64_t mod>
struct modint {
    using LL = int64_t;
    LL val;
    modint(LL val=0) : val(((val % mod) + mod) % mod) {}

    const modint operator+() const { return *this; }
    const modint operator-() const { return (-val + mod) % mod; }
    const modint inv() const { return pow(mod-2); }

    modint& operator+=(const modint& rhs) {
        (val += rhs.val) %= mod;
        return *this;
    }
    modint& operator-=(const modint& rhs) {
        return *this += -rhs;
    }
    modint& operator*=(const modint& rhs) {
        (val *= rhs.val) %= mod;
        return *this;
    }
    modint& operator/=(const modint& rhs) {
        return *this *= rhs.inv();
    }

    const modint operator+(const modint& rhs) const {
        return modint(*this) += rhs;
    }
    const modint operator-(const modint& rhs) const {
        return modint(*this) -= rhs;
    }
    const modint operator*(const modint& rhs) const {
        return modint(*this) *= rhs;
    }
    const modint operator/(const modint& rhs) const {
        return modint(*this) /= rhs;
    }

    const modint pow(LL n) const {
        modint ret = 1, tmp = val;
        while (n) {
            if (n & 1) ret *= tmp;
            tmp *= tmp; n >>= 1;
        }
        return ret;
    }

    bool operator==(const modint& rhs) const { return val == rhs.val; }
    bool operator!=(const modint& rhs) const { return !(*this == rhs); }

    friend const modint operator+(const LL& lhs, const modint& rhs) {
        return modint(lhs) + rhs;
    }
    friend const modint operator-(const LL& lhs, const modint& rhs) {
        return modint(lhs) - rhs;
    }
    friend const modint operator*(const LL& lhs, const modint& rhs) {
        return modint(lhs) * rhs;
    }
    friend const modint operator/(const LL& lhs, const modint& rhs) {
        return modint(lhs) / rhs;
    }

    friend bool operator==(const LL& lhs, const modint& rhs) {
        return modint(lhs) == rhs;
    }
    friend bool operator!=(const LL& lhs, const modint& rhs) {
        return modint(lhs) != rhs;
    }

    friend ostream& operator<<(ostream& os, const modint& a) {
        return os << a.val;
    }
    friend istream& operator>>(istream& is, modint& a) {
        LL tmp; is >> tmp;
        a = tmp;
        return is;
    }
};


template<typename T>
struct Matrix {
    vector<vector<T>> A;

    Matrix() {}

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

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

    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 I(size_t n) {
        Matrix B(n);
        for (int i = 0; i < n; ++i) B[i][i] = 1;
        return (B);
    }

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

    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)
                A[i][j] += B[i][j];
        return (*this);
    }

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

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

    Matrix pow(int64_t k) {
        Matrix B = Matrix::I(height()), tmp = *this;
        while (k) {
            if (k & 1) B *= tmp;
            tmp *= tmp; k >>= 1;
        }
        return (B);
    }

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

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

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

    int GaussJordanElimination() {
        int rank = 0;
        for (int col = 0; col < width(); ++col) {
            int pivot = -1;
            for (int row = rank; row < height(); ++row) {
                if (A[row][col] != 0) {
                    pivot = row;
                    break;
                }
            }
            if (pivot == -1) continue;
            swap(A[rank], A[pivot]);
            T topLeft = A[rank][col];
            for (int c = col; c < width(); ++c) {
                A[rank][c] /= topLeft;
            }
            for (int row = rank+1; row < height(); ++row) {
                T ratio = A[row][col];
                for (int c = col; c < width(); ++c)
                    A[row][c] -= ratio * A[rank][c];
            }
            ++rank;
        }
        return (rank);
    }

    friend istream& operator>>(istream& is, Matrix& B) {
        is >> B.A;
        return (is);
    }

    friend ostream& operator<<(ostream& os, Matrix& B) {
        size_t n = B.height(), m = B.width();
        for (int i = 0; i < n; ++i) {
            os << (i == 0 ? "[" : " ");
            for (int j = 0; j < m; ++j) {
                os << B[i][j] << (j == m-1 ? "]" : ",");
            }
            os << (i == n-1 ? "]\n" : ",\n");
        }
        return (os);
    }
};


int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);

    // ifstream in("in.txt");
    // cin.rdbuf(in.rdbuf());

    ll M, K; cin >> M >> K;

    using Int = modint<MOD>;

    Matrix<Int> A(M, M);
    REP(i, M) {
        REP(j, M) {
            A[i][(i + j) % M] += 1;
            A[i][(i * j) % M] += 1;
        }
    }

    Matrix<Int> p(1, M);
    p[0][0] = 1;

    p = p * A.pow(K);

    cout << p[0][0] << endl;

    return 0;
}
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