結果

問題 No.2487 Multiple of M
ユーザー square1001square1001
提出日時 2023-09-30 00:08:47
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 2 ms / 2,000 ms
コード長 3,199 bytes
コンパイル時間 1,909 ms
コンパイル使用メモリ 207,224 KB
最終ジャッジ日時 2025-02-17 03:42:03
ジャッジサーバーID
(参考情報)
judge2 / judge5
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
sample AC * 3
other AC * 53
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

#include <bits/stdc++.h>
using namespace std;
#ifndef CLASS_MODINT
#define CLASS_MODINT
#include <cstdint>
template <std::uint32_t mod>
class modint {
private:
std::uint32_t n;
public:
modint() : n(0) {};
modint(std::int64_t n_) : n((n_ >= 0 ? n_ : mod - (-n_) % mod) % mod) {};
static constexpr std::uint32_t get_mod() { return mod; }
std::uint32_t get() const { return n; }
bool operator==(const modint& m) const { return n == m.n; }
bool operator!=(const modint& m) const { return n != m.n; }
modint& operator+=(const modint& m) { n += m.n; n = (n < mod ? n : n - mod); return *this; }
modint& operator-=(const modint& m) { n += mod - m.n; n = (n < mod ? n : n - mod); return *this; }
modint& operator*=(const modint& m) { n = std::uint64_t(n) * m.n % mod; return *this; }
modint operator+(const modint& m) const { return modint(*this) += m; }
modint operator-(const modint& m) const { return modint(*this) -= m; }
modint operator*(const modint& m) const { return modint(*this) *= m; }
modint inv() const { return (*this).pow(mod - 2); }
modint pow(std::uint64_t b) const {
modint ans = 1, m = modint(*this);
while (b) {
if (b & 1) ans *= m;
m *= m;
b >>= 1;
}
return ans;
}
};
#endif // CLASS_MODINT
using mint = modint<998244353>;
long long mygcd(long long x, long long y) {
if (y == 0) {
return x;
}
return mygcd(y, x % y);
}
array<mint, 2> merge(long long X, const array<mint, 2>& v1, const array<mint, 2>& v2) {
array<mint, 2> res = { mint(0), mint(0) };
res[1] += v1[1] * v2[1];
res[0] += v1[0] * v2[1];
res[0] += v1[1] * v2[0];
res[0] += v1[0] * v2[0] * (X - 2);
res[1] += v1[0] * v2[0] * (X - 1);
return res;
}
mint solve(long long N, long long M, long long K) {
long long cur = 1;
vector<long long> seq = { 1 };
while (true) {
cur = mygcd(cur * K, M);
if (cur == seq.back()) {
break;
}
seq.push_back(cur);
}
if (seq.size() > N) {
seq.resize(N);
}
int V = seq.size();
seq.push_back(M);
vector<long long> d(V);
for (int i = 0; i < V; i++) {
d[i] = seq[i + 1] / seq[i];
}
vector<vector<mint> > dp(V);
dp[0] = { mint(1) };
for (int i = 1; i < V; i++) {
dp[i].resize(i + 1);
for (int j = 0; j < i; j++) {
dp[i][j + 1] += dp[i - 1][j] * seq[i - 1];
dp[i][j] += dp[i - 1][j];
}
for (int j = 0; j <= i; j++) {
dp[i][j] *= (j >= 1 ? mint(d[i - 1]).pow(j - 1) : mint(1));
}
}
array<mint, 2> ini = { mint(0), mint(0) };
for (int i = 0; i < V; i++) {
array<mint, 2> sub;
sub[0] = dp[V - 1][i] * (i >= 1 ? mint(d[V - 1]).pow(i - 1) : mint(0));
sub[1] = dp[V - 1][i] * (i >= 1 ? mint(d[V - 1]).pow(i - 1) : mint(1));
if ((V - i - 1) % 2 == 0) {
ini[0] += sub[0];
ini[1] += sub[1];
}
else {
ini[0] -= sub[0];
ini[1] -= sub[1];
}
}
array<mint, 2> g = { seq[V - 1], seq[V - 1] - 1 };
array<mint, 2> v = { mint(0), mint(1) };
long long X = M / seq[V - 1];
long long rem = N - V + 1;
while (rem >= 1) {
if (rem % 2 == 1) {
v = merge(X, g, v);
}
g = merge(X, g, g);
rem /= 2;
}
array<mint, 2> ans = merge(X, ini, v);
return ans[1];
}
int main() {
long long N, M, K;
cin >> N >> M >> K;
mint ans = solve(N, M, K);
cout << ans.get() << endl;
return 0;
}
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