結果

問題 No.2883 K-powered Sum of Fibonacci
ユーザー SnowBeenDidingSnowBeenDiding
提出日時 2024-09-09 03:55:35
言語 C++23
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 503 ms / 3,000 ms
コード長 5,019 bytes
コンパイル時間 5,734 ms
コンパイル使用メモリ 314,192 KB
実行使用メモリ 42,564 KB
最終ジャッジ日時 2024-09-09 03:55:51
合計ジャッジ時間 15,039 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge2
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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 60 ms
42,260 KB
testcase_01 AC 60 ms
42,232 KB
testcase_02 AC 74 ms
42,380 KB
testcase_03 AC 58 ms
42,336 KB
testcase_04 AC 60 ms
42,284 KB
testcase_05 AC 84 ms
42,348 KB
testcase_06 AC 60 ms
42,380 KB
testcase_07 AC 160 ms
42,412 KB
testcase_08 AC 78 ms
42,292 KB
testcase_09 AC 68 ms
42,372 KB
testcase_10 AC 68 ms
42,376 KB
testcase_11 AC 286 ms
42,348 KB
testcase_12 AC 80 ms
42,332 KB
testcase_13 AC 68 ms
42,288 KB
testcase_14 AC 333 ms
42,396 KB
testcase_15 AC 124 ms
42,440 KB
testcase_16 AC 59 ms
42,224 KB
testcase_17 AC 91 ms
42,272 KB
testcase_18 AC 64 ms
42,288 KB
testcase_19 AC 96 ms
42,396 KB
testcase_20 AC 436 ms
42,564 KB
testcase_21 AC 379 ms
42,412 KB
testcase_22 AC 427 ms
42,352 KB
testcase_23 AC 360 ms
42,392 KB
testcase_24 AC 339 ms
42,512 KB
testcase_25 AC 448 ms
42,512 KB
testcase_26 AC 490 ms
42,564 KB
testcase_27 AC 452 ms
42,400 KB
testcase_28 AC 456 ms
42,344 KB
testcase_29 AC 503 ms
42,416 KB
testcase_30 AC 60 ms
42,352 KB
testcase_31 AC 59 ms
42,360 KB
testcase_32 AC 60 ms
42,384 KB
testcase_33 AC 69 ms
42,412 KB
testcase_34 AC 59 ms
42,396 KB
testcase_35 AC 61 ms
42,224 KB
testcase_36 AC 59 ms
42,332 KB
testcase_37 AC 60 ms
42,468 KB
testcase_38 AC 59 ms
42,328 KB
testcase_39 AC 59 ms
42,388 KB
testcase_40 AC 60 ms
42,264 KB
testcase_41 AC 60 ms
42,432 KB
testcase_42 AC 477 ms
42,488 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 <atcoder/all>
#include <bits/stdc++.h>
#define rep(i, a, b) for (ll i = (ll)(a); i < (ll)(b); i++)
using namespace atcoder;
using namespace std;

typedef long long ll;

using mint = modint998244353;

struct Comb {
    vector<mint> fact, ifact;
    int MAX_COM;
    Comb() {}
    Comb(int n) {
        MAX_COM = n; // ここでMAX入力を調整
        init(998244353, MAX_COM);
    }
    void init(long long MOD, long long MAX_COM) {
        int n = MAX_COM;
        assert(n < MOD);
        fact = vector<mint>(n + 1);
        ifact = vector<mint>(n + 1);
        fact[0] = 1;
        for (int i = 1; i <= n; ++i)
            fact[i] = fact[i - 1] * i;
        ifact[n] = fact[n].inv();
        for (int i = n; i >= 1; --i)
            ifact[i - 1] = ifact[i] * i;
    }
    mint operator()(long long n, long long k) {
        if (k < 0 || k > n)
            return 0;
        return fact[n] * ifact[k] * ifact[n - k];
    }
};
Comb comb(5000010);

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

    Matrix() {}

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

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

    T zero() { return (T(0)); }

    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 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() && 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() && 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, zero()));
        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::I(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); }

    bool operator==(const Matrix &B) const {
        size_t n = height(), m = width();
        if (n != B.height() || m != B.width())
            return false;
        for (int i = 0; i < n; i++)
            for (int j = 0; j < m; j++)
                if ((*this)[i][j] != B[i][j])
                    return false;
        return true;
    }

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

    T determinant() { // O(n^3)
        Matrix B(*this);
        assert(width() == height());
        T ret = 1;
        for (int i = 0; i < width(); i++) {
            int idx = -1;
            for (int j = i; j < width(); j++) {
                if (B[j][i] != 0)
                    idx = j;
            }
            if (idx == -1)
                return (0);
            if (i != idx) {
                ret *= -1;
                swap(B[i], B[idx]);
            }
            ret *= B[i][i];
            T vv = B[i][i];
            for (int j = 0; j < width(); j++) {
                B[i][j] /= vv;
            }
            for (int j = i + 1; j < width(); j++) {
                T a = B[j][i];
                for (int k = 0; k < width(); k++) {
                    B[j][k] -= B[i][k] * a;
                }
            }
        }
        return (ret);
    }
};

void solve(ll n, int k) {
    Matrix<mint> C(k + 2);
    rep(i, 0, k + 1) rep(j, 0, k + 1) C[i][j] = comb(k - i, k - j - i);
    C[k + 1][k + 1] = 1;
    C[k + 1][0] = 1;
    C ^= n - 1;
    mint ans = 0;
    rep(i, 0, k + 2) ans += C[k + 1][i];
    cout << ans.val() << endl;
}

int main() {
    ll n;
    int k;
    cin >> n >> k;
    solve(n, k);
}
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