結果

問題 No.2857 Div Array
ユーザー t98slidert98slider
提出日時 2024-08-25 20:35:42
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
AC  
実行時間 27 ms / 2,000 ms
コード長 5,493 bytes
コンパイル時間 2,176 ms
コンパイル使用メモリ 210,448 KB
実行使用メモリ 6,944 KB
最終ジャッジ日時 2024-08-25 20:35:46
合計ジャッジ時間 3,786 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge2
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ファイルパターン 結果
other AC * 30
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;
using ll = long long;

template<class T> ostream& operator << (ostream& os, const vector<T>& vec) {
	if(vec.empty()) return os;
	os << vec[0];
	for(auto it = vec.begin(); ++it != vec.end(); ) os << ' ' << *it;
	return os;
}

template<const unsigned int MOD> struct prime_modint {
	using mint = prime_modint;
	unsigned int v;
	prime_modint() : v(0) {}
	prime_modint(unsigned int a) { a %= MOD; v = a; }
	prime_modint(unsigned long long a) { a %= MOD; v = a; }
	prime_modint(int a) { a %= (int)(MOD); if(a < 0)a += MOD; v = a; }
	prime_modint(long long a) { a %= (int)(MOD); if(a < 0)a += MOD; v = a; }
	static constexpr int mod() { return MOD; }
	mint& operator++() {v++; if(v == MOD)v = 0; return *this;}
	mint& operator--() {if(v == 0)v = MOD; v--; return *this;}
	mint operator++(int) { mint result = *this; ++*this; return result; }
	mint operator--(int) { mint result = *this; --*this; return result; }
	mint& operator+=(const mint& rhs) { v += rhs.v; if(v >= MOD) v -= MOD; return *this; }
	mint& operator-=(const mint& rhs) { if(v < rhs.v) v += MOD; v -= rhs.v; return *this; }
	mint& operator*=(const mint& rhs) {
		v = (unsigned int)((unsigned long long)(v) * rhs.v % MOD);
		return *this;
	}
	mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
	mint operator+() const { return *this; }
	mint operator-() const { return mint() - *this; }
	mint pow(long long n) const {
		assert(0 <= n);
		mint r = 1, x = *this;
		while (n) {
			if (n & 1) r *= x;
			x *= x;
			n >>= 1;
		}
		return r;
	}
	mint inv() const { assert(v); return pow(MOD - 2); }
	friend mint operator+(const mint& lhs, const mint& rhs) { return mint(lhs) += rhs; }
	friend mint operator-(const mint& lhs, const mint& rhs) { return mint(lhs) -= rhs; }
	friend mint operator*(const mint& lhs, const mint& rhs) { return mint(lhs) *= rhs; }
	friend mint operator/(const mint& lhs, const mint& rhs) { return mint(lhs) /= rhs; }
	friend bool operator==(const mint& lhs, const mint& rhs) { return (lhs.v == rhs.v); }
	friend bool operator!=(const mint& lhs, const mint& rhs) { return (lhs.v != rhs.v); }
	friend std::ostream& operator << (std::ostream &os, const mint& rhs) noexcept { return os << rhs.v; }
};
//using mint = prime_modint<1000000007>;
using mint = prime_modint<998244353>;

template <class T, size_t N> struct Matrix {
    std::array<std::array<T, N>, N> A{};
    Matrix() {}
    Matrix(const std::array<std::array<T, N>, N> &M) : A(M){}
    Matrix(const std::vector<std::vector<T>> &M)  {
        for(size_t i = 0; i < N; i++){
            for(size_t j = 0; j < N; j++){
                A[i][j] = M[i][j];
            }
        }
    }
    const std::array<T, N>& operator[](int i) const { return A[i]; }
    std::array<T, N>& operator[](int i) { return A[i]; }

    Matrix& operator+=(const Matrix& rhs) {
        for(size_t i = 0; i < N; i++){
            for(size_t j = 0; j < N; j++){
                A[i][j] += rhs[i][j];
            }
        }
        return *this;
    }
    Matrix& operator-=(const Matrix& rhs) {
        for(size_t i = 0; i < N; i++){
            for(size_t j = 0; j < N; j++){
                A[i][j] -= rhs[i][j];
            }
        }
        return *this;
    }
    Matrix& operator*=(const Matrix& rhs) {
        std::array<std::array<T, N>, N> res{};
        for(size_t i = 0; i < N; i++){
            for(size_t k = 0; k < N; k++){
                for(size_t j = 0; j < N; j++){
                    res[i][j] += A[i][k] * rhs[k][j];
                }
            }
        }
        swap(A, res);
        return *this;
    }
    Matrix& operator+() const { return *this; }
    Matrix& operator-() const { return Matrix() - *this; }
    friend Matrix operator+(const Matrix& lhs, const Matrix& rhs) {
        return Matrix(lhs) += rhs;
    }
    friend Matrix operator-(const Matrix& lhs, const Matrix& rhs) {
        return Matrix(lhs) -= rhs;
    }
    friend Matrix operator*(const Matrix& lhs, const Matrix& rhs) {
        return Matrix(lhs) *= rhs;
    }
    friend bool operator==(const Matrix& lhs, const Matrix& rhs) {
        return (lhs.A == rhs.A);
    }
    friend bool operator!=(const Matrix& lhs, const Matrix& rhs) {
        return (lhs.A != rhs.A);
    }
    Matrix pow(long long v){
        Matrix res, temp = A;
        for(size_t i = 0; i < N; i++)res[i][i] = 1;
        while(v){
            if(v & 1)res *= temp;
            temp *= temp;
            v >>= 1;
        }
        return res;
    }
    friend std::ostream& operator << (std::ostream &os, const Matrix& rhs) noexcept {
        for(size_t i = 0; i < N; i++){
            if(i) os << '\n';
            for(size_t j = 0; j < N; j++){
                os << (j ? " " : "") << rhs[i][j];
            }
        }
        return os;
    }
};

int main(){
	ios::sync_with_stdio(false);
	cin.tie(0);
	int n, m, k;
	cin >> n >> m >> k;
	if(n == 1){
		cout << m << '\n';
		return 0;
	}
	vector<int> c(m), d;
	for(int i = 1; i <= m; i++){
		c[m - i] = m / i;
	}
	d = c;
	d.erase(unique(d.begin(), d.end()), d.end());
	int M = d.size();
	vector<int> cnt(M);
	for(int i = 1, di = M - 1; i <= m; i++){
		while(d[di] > c[m - i]) di--;
		cnt[di]++;
	}
	Matrix<mint, 64> Mt;
	for(int y = 0; y < M; y++){
		for(int x = 0; x < M; x++){
			if(abs(d[y] - d[x]) <= k) Mt[y][x] = cnt[x];
		}
	}
	auto B = Mt.pow(n - 1);
	mint ans;
	for(int y = 0; y < M; y++){
		for(int x = 0; x < M; x++){
			ans += cnt[y] * B[y][x];
		}
	}
	cout << ans << '\n';
}
0