結果

問題 No.2857 Div Array
ユーザー shinchan
提出日時 2024-08-25 14:14:58
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
AC  
実行時間 169 ms / 2,000 ms
コード長 2,297 bytes
コンパイル時間 21,043 ms
コンパイル使用メモリ 340,436 KB
最終ジャッジ日時 2025-02-24 01:06:42
ジャッジサーバーID
(参考情報)
judge2 / judge1
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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 #
プレゼンテーションモードにする

#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
#include <atcoder/convolution>
#include <atcoder/modint>
using namespace std;
using namespace atcoder;
#define rep(i, n) for(int i=0;i<n;i++)
using mint = modint998244353;
vector<mint> BerlekampMassey(const vector<mint> &s) {
const int N = (int)s.size();
vector<mint> b, c;
b.reserve(N + 1);
c.reserve(N + 1);
b.push_back(mint(1));
c.push_back(mint(1));
mint y = mint(1);
for (int ed = 1; ed <= N; ed++) {
int l = int(c.size()), m = int(b.size());
mint x = 0;
for (int i = 0; i < l; i++) x += c[i] * s[ed - l + i];
b.emplace_back(mint(0));
m++;
if (x == mint(0)) continue;
mint freq = x / y;
if (l < m) {
auto tmp = c;
c.insert(begin(c), m - l, mint(0));
for (int i = 0; i < m; i++) c[m - 1 - i] -= freq * b[m - 1 - i];
b = tmp;
y = x;
} else {
for (int i = 0; i < m; i++) c[l - 1 - i] -= freq * b[m - 1 - i];
}
}
reverse(begin(c), end(c));
return c;
}
template <typename T> T BostanMori(std::vector<T> Q, std::vector<T> P, long long N) {
const int d = Q.size();
for (; N; N >>= 1) {
auto Q_neg = Q;
for (size_t i = 1; i < Q.size(); i += 2) Q_neg[i] *= -1;
P = convolution(P, Q_neg);
Q = convolution(Q, Q_neg);
for (size_t i = N & 1; i < P.size(); i += 2) P[i >> 1] = P[i];
for (size_t i = 0; i < Q.size(); i += 2) Q[i >> 1] = Q[i];
P.resize(d - 1);
Q.resize(d);
}
return P[0];
}
using ll = long long;
int main() {
ll n, m, k; cin >> n >> m >> k;
ll N = 10000;
vector<mint> v(N);
v[0] = 1;
v[1] = m;
vector<mint> dp(m + 1, 0);
for(ll i = 1; i <= m; i ++) dp[m / i] ++;
for(int i = 2; i < N; i ++) {
rep(j, m) dp[j + 1] += dp[j];
vector<mint> nx(m + 1, 0);
for(ll j = 1; j <= m; j ++) {
ll num = m / j;
nx[num] += dp[min(m, num + k)] - dp[max(0LL, num - k - 1)];
}
swap(nx, dp);
rep(j, m + 1) v[i] += dp[j];
}
vector<mint> a = BerlekampMassey(v);
vector<mint> b = convolution(v, a);
b.resize(a.size() - 1);
cout << BostanMori(a, b, n).val() << "\n";
return 0;
}
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