#979962 (C++17) No.2857 Div Array

• 問題: No.2857 Div Array
• ユーザー: dyktr_06
• 提出日時: 2024-05-09 22:35:53
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 26 ms / 2,000 ms
• コード長: 10,934 bytes
• コンパイル時間: 2,421 ms
• コンパイル使用メモリ: 215,580 KB
• 実行使用メモリ: 5,376 KB
• 最終ジャッジ日時: 2024-05-09 22:35:58
• 合計ジャッジ時間: 3,458 ms
• ジャッジサーバーID （参考情報）: judge5 / judge3

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 5,248 KB
testcase_01	AC	2 ms; 5,376 KB
testcase_02	AC	2 ms; 5,376 KB
testcase_03	AC	2 ms; 5,376 KB
testcase_04	AC	1 ms; 5,376 KB
testcase_05	AC	1 ms; 5,376 KB
testcase_06	AC	2 ms; 5,376 KB
testcase_07	AC	2 ms; 5,376 KB
testcase_08	AC	1 ms; 5,376 KB
testcase_09	AC	2 ms; 5,376 KB
testcase_10	AC	2 ms; 5,376 KB
testcase_11	AC	21 ms; 5,376 KB
testcase_12	AC	6 ms; 5,376 KB
testcase_13	AC	3 ms; 5,376 KB
testcase_14	AC	20 ms; 5,376 KB
testcase_15	AC	3 ms; 5,376 KB
testcase_16	AC	1 ms; 5,376 KB
testcase_17	AC	17 ms; 5,376 KB
testcase_18	AC	16 ms; 5,376 KB
testcase_19	AC	10 ms; 5,376 KB
testcase_20	AC	26 ms; 5,376 KB
testcase_21	AC	26 ms; 5,376 KB
testcase_22	AC	26 ms; 5,376 KB
testcase_23	AC	25 ms; 5,376 KB
testcase_24	AC	2 ms; 5,376 KB
testcase_25	AC	2 ms; 5,376 KB
testcase_26	AC	2 ms; 5,376 KB
testcase_27	AC	2 ms; 5,376 KB
testcase_28	AC	2 ms; 5,376 KB
testcase_29	AC	1 ms; 5,376 KB

ソースコード

#include <bits/stdc++.h>
using namespace std;

template <long long Modulus>
struct ModInt{
    long long val;
    constexpr ModInt(const long long _val = 0) noexcept : val(_val) {
        normalize();
    }
    void normalize(){
        val = (val % Modulus + Modulus) % Modulus;
    }
    inline ModInt &operator+=(const ModInt &rhs) noexcept {
        if(val += rhs.val, val >= Modulus) val -= Modulus;
        return *this;
    }
    inline ModInt &operator-=(const ModInt &rhs) noexcept {
        if(val -= rhs.val, val < 0) val += Modulus;
        return *this;
    }
    inline ModInt &operator*=(const ModInt &rhs) noexcept {
        val = val * rhs.val % Modulus;
        return *this;
    }
    inline ModInt &operator/=(const ModInt &rhs) noexcept {
        val = val * inv(rhs.val).val % Modulus;
        return *this;
    }
    inline ModInt &operator++() noexcept {
        if(++val >= Modulus) val -= Modulus;
        return *this;
    }
    inline ModInt operator++(int) noexcept {
        ModInt t = val;
        if(++val >= Modulus) val -= Modulus;
        return t;
    }
    inline ModInt &operator--() noexcept {
        if(--val < 0) val += Modulus;
        return *this;
    }
    inline ModInt operator--(int) noexcept {
        ModInt t = val;
        if(--val < 0) val += Modulus;
        return t;
    }
    inline ModInt operator-() const noexcept { return (Modulus - val) % Modulus; }
    inline ModInt inv(void) const { return inv(val); }
    ModInt pow(long long n){
        assert(0 <= n);
        ModInt x = *this, r = 1;
        while(n){
            if(n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    ModInt inv(const long long n) const {
        long long a = n, b = Modulus, u = 1, v = 0;
        while(b){
            long long t = a / b;
            a -= t * b; swap(a, b);
            u -= t * v; swap(u, v);
        }
        u %= Modulus;
        if(u < 0) u += Modulus;
        return u;
    }
    friend inline ModInt operator+(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) += rhs; }
    friend inline ModInt operator-(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) -= rhs; }
    friend inline ModInt operator*(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) *= rhs; }
    friend inline ModInt operator/(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) /= rhs; }
    friend inline bool operator==(const ModInt &lhs, const ModInt &rhs) noexcept { return lhs.val == rhs.val; }
    friend inline bool operator!=(const ModInt &lhs, const ModInt &rhs) noexcept { return lhs.val != rhs.val; }
    friend inline istream &operator>>(istream &is, ModInt &x) noexcept {
        is >> x.val;
        x.normalize();
        return is;
    }
    friend inline ostream &operator<<(ostream &os, const ModInt &x) noexcept { return os << x.val; }
};

template <typename T>
struct Matrix{
    int n, m;
    vector<T> val;
    Matrix(int _n, int _m) : n(_n), m(_m), val(_n *_m){}
    Matrix(const vector<vector<T>> &mat){
        n = mat.size();
        m = mat[0].size();
        val.resize(n * m);
        for(int i = 0; i < n; ++i){
            for(int j = 0; j < m; ++j){
                val[i * m + j] = mat[i][j];
            }
        }
    }
    static Matrix e(int _n){
        Matrix res(_n, _n);
        for(int i = 0; i < _n; ++i){
            res[i][i] = T{1};
        }
        return res;
    }
    auto operator[](int i){ return val.begin() + i * m; }
    auto operator[](int i) const { return val.begin() + i * m; }
    inline Matrix &operator+=(const Matrix &rhs){
        for(int i = 0; i < n * m; ++i){
            val[i] += rhs[i];
        }
        return *this;
    }
    inline Matrix &operator-=(const Matrix &rhs){
        for(int i = 0; i < n * m; ++i){
            val[i] -= rhs[i];
        }
        return *this;
    }
    inline Matrix operator*(const Matrix &rhs){
        assert(m == rhs.n);
        const int l = rhs.m;
        Matrix res(n, l);
        for(int i = 0; i < n; ++i){
            for(int j = 0; j < m; ++j){
                for(int k = 0; k < l; ++k){
                    res[i][k] += val[i * m + j] * rhs[j][k];
                }
            }
        }
        return res;
    }
    inline Matrix &operator*=(const Matrix &rhs){
        return *this = *this * rhs;
    }
    friend inline Matrix operator+(const Matrix &lhs, const Matrix &rhs) noexcept { return Matrix(lhs) += rhs; }
    friend inline Matrix operator-(const Matrix &lhs, const Matrix &rhs) noexcept { return Matrix(lhs) -= rhs; }
    friend inline bool operator==(const Matrix &lhs, const Matrix &rhs) noexcept { return lhs.val == rhs.val; }
    friend inline bool operator!=(const Matrix &lhs, const Matrix &rhs) noexcept { return lhs.val != rhs.val; }
    friend inline ostream &operator<<(ostream &os, const Matrix &mat) noexcept {
        const int _n = mat.n;
        const int _m = mat.m;
        for(int i = 0; i < _n; ++i){
            for(int j = 0; j < _m; ++j){
                os << mat[i][j] << " \n"[j == _m - 1];
            }
        }
        return os;
    }
    Matrix inv() const {
        Matrix a = *this, b = e(n);
        for(int i = 0; i < n; ++i){
            if(a[i][i] == 0){
                for(int j = i + 1; j < n; ++j){
                    if(a[j][i] != 0){
                        for(int k = i; k < n; ++k) swap(a[i][k], a[j][k]);
                        for(int k = 0; k < n; ++k) swap(b[i][k], b[j][k]);
                        break;
                    }
                }
            }
            if(a[i][i] == 0) throw "Inverse does not exist.";
            const T x = T{1} / a[i][i];
            for(int k = i; k < n; ++k) a[i][k] *= x;
            for(int k = 0; k < n; ++k) b[i][k] *= x;
            for(int j = 0; j < n; ++j){
                if(i != j){
                    const T x = a[j][i];
                    for(int k = i; k < n; ++k) a[j][k] -= a[i][k] * x;
                    for(int k = 0; k < n; ++k) b[j][k] -= b[i][k] * x;
                }
            }
        }
        return b;
    }
    Matrix pow(long long r) const {
        if(r == 0) return e(n);
        if(r < 0) return inv().pow(-r);
        Matrix res = e(n), a = *this;
        while(r > 0){
            if(r & 1) res *= a;
            a *= a;
            r >>= 1;
        }
        return res;
    }
    Matrix pow2(string &r) const {
        if(r == "0") return e(n);
        Matrix res = e(n), a = *this;
        int siz = r.size();
        for(int i = siz - 1; i >= 0; i--){
            if(r[i] == '1') res *= a;
            a *= a;
        }
        return res;
    }
    T det() const {
        Matrix a = *this;
        T res = 1;
        for(int i = 0; i < n; ++i){
            if(a[i][i] == 0){
                for(int j = i + 1; j < n; ++j){
                    if(a[j][i] != 0){
                        for(int k = i; k < n; ++k){
                            swap(a[i][k], a[j][k]);
                        }
                        res = -res;
                        break;
                    }
                }
            }
            if(a[i][i] == 0) return 0;
            res *= a[i][i];
            const T x = T{1} / a[i][i];
            for(int k = i; k < n; ++k){
                a[i][k] *= x;
            }
            for(int j = i + 1; j < n; ++j){
                const T x = a[j][i];
                for(int k = i; k < n; ++k){
                    a[j][k] -= a[i][k] * x;
                }
            }
        }
        return res;
    }
    Matrix transpose() const {
        Matrix res(m, n), a = *this;
        for(int i = 0; i < n; ++i){
            for(int j = 0; j < m; ++j){
                res[j][i] = a[i][j];
            }
        }
        return res;
    }
    Matrix gauss() const {
        Matrix a = *this;
        int r = 0;
        for(int i = 0; i < m; ++i){
            int pivot = -1;
            for(int j = r; j < n; ++j){
                if(a[j][i] != 0){
                    pivot = j;
                    break;
                }
            }
            if(pivot == -1) continue;
            for(int j = 0; j < m; ++j){
                swap(a[pivot][j], a[r][j]);
            }
            const T s = a[r][i];
            for(int j = i; j < m; ++j){
                a[r][j] /= s;
            }
            for(int j = 0; j < n; ++j){
                if(j == r) continue;
                const T s = a[j][i];
                if(s == 0) continue;
                for(int k = i; k < m; ++k){
                    a[j][k] -= a[r][k] * s;
                }
            }
            ++r;
        }
        return a;
    }
    int rank(bool is_gaussed = false) const {
        Matrix a = *this;
        if(!is_gaussed){
            return (n >= m ? a : a.transpose()).gauss().rank(true);
        }
        int r = 0;
        for(int i = 0; i < n; ++i){
            while(r < m && a[i][r] == 0) ++r;
            if(r == m){
                return i;
            }
            ++r;
        }
        return n;
    }
    // Rotate 90 degrees clockwise
    Matrix rotate() const {
        Matrix res(m, n), a = *this;
        for(int i = 0; i < m; ++i){
            for(int j = 0; j < n; ++j){
                res[i][j] = a[n - j - 1][i];
            }
        }
        return res;
    }
};

template <typename T>
struct compress{
    vector<T> sorted;
    vector<int> compressed;

    compress(const vector<T> &vec){
        int n = vec.size();
        compressed.resize(n);
        for(T x : vec){
            sorted.emplace_back(x);
        }
        sort(sorted.begin(), sorted.end());
        sorted.erase(unique(sorted.begin(), sorted.end()), sorted.end());
        for(int i = 0; i < n; ++i){
            compressed[i] = lower_bound(sorted.begin(), sorted.end(), vec[i]) - sorted.begin();
        }
    }

    int get(const T &x) const{
        return lower_bound(sorted.begin(), sorted.end(), x) - sorted.begin();
    }

    T inv(const int x) const{
        return sorted[x];
    }

    size_t size() const{
        return sorted.size();
    }

    vector<T> getCompressed() const{
        return compressed;
    }
};

using mint = ModInt<998244353>;

int main(){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    long long n;
    int m, k;
    cin >> n >> m >> k;

    vector<int> q;
    for(int i = 1; i <= m; i++){
        q.push_back(m / i);
    }
    compress<int> comp(q);
    int siz = comp.size();

    Matrix<mint> dp(siz, siz), mat(1, siz);
    for(int i = 0; i < siz; i++){
        for(int j = 1; j <= m; j++){
            if(abs(m / j - comp.inv(i)) <= k){
                dp[i][comp.get(m / j)]++;
            }
        }
    }

    for(int i = 1; i <= m; i++){
        mat[0][comp.get(m / i)] += 1;
    }

    dp = dp.pow(n - 1);
    mat *= dp;

    mint ans = 0;
    for(int i = 0; i < siz; i++){
        ans += mat[0][i];
    }
    cout << ans << "\n";
}