結果
問題 | No.2857 Div Array |
ユーザー |
|
提出日時 | 2024-05-09 22:35:53 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 29 ms / 2,000 ms |
コード長 | 10,934 bytes |
コンパイル時間 | 2,680 ms |
コンパイル使用メモリ | 209,284 KB |
最終ジャッジ日時 | 2025-02-21 12:05:22 |
ジャッジサーバーID (参考情報) |
judge1 / judge4 |
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ファイルパターン | 結果 |
---|---|
other | AC * 30 |
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 clockwiseMatrix 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";}