結果

問題 No.1396 Giri
コンテスト
ユーザー tkmst201
提出日時 2021-02-15 19:13:02
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 460 ms / 2,000 ms
コード長 4,715 bytes
コンパイル時間 2,757 ms
コンパイル使用メモリ 204,448 KB
最終ジャッジ日時 2025-01-18 21:12:41
ジャッジサーバーID
（参考情報） 		judge4 / judge1
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ファイルパターン 結果
sample AC * 3
other AC * 23
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;
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) begin(v),end(v)
template<typename A, typename B> inline bool chmax(A & a, const B & b) { if (a < b) { a = b; return true; } return false; }
template<typename A, typename B> inline bool chmin(A & a, const B & b) { if (a > b) { a = b; return true; } return false; }
using ll = long long;
using pii = pair<int, int>;
constexpr ll INF = 1ll<<30;
constexpr ll longINF = 1ll<<60;
constexpr ll MOD = 998244353;
constexpr bool debug = false;
//---------------------------------//

template<int M>
struct ModInt {
	static_assert(M > 0);
	
public:
	using value_type = int;
	using calc_type = std::int_fast64_t;
	
private:
	value_type val_;
	
public:
	constexpr ModInt(calc_type val = 0) : val_(val < 0 ? (val % M + M) % M : val % M) {}
	constexpr const value_type & val() const noexcept { return val_; }
	constexpr static decltype(M) mod() noexcept { return M; }
	
	explicit constexpr operator bool() const noexcept { return val_; }
	constexpr bool operator !() const noexcept { return !static_cast<bool>(*this); }
	constexpr ModInt operator +() const noexcept { return ModInt(*this); }
	constexpr ModInt operator -() const noexcept { return ModInt(-val_); }
	constexpr ModInt operator ++(int) noexcept { ModInt res = *this; ++*this; return res; }
	constexpr ModInt operator --(int) noexcept { ModInt res = *this; --*this; return res; }
	constexpr ModInt & operator ++() noexcept { val_ = val_ + 1 == M ? 0 : val_ + 1; return *this; }
	constexpr ModInt & operator --() noexcept { val_ = val_ == 0 ? M - 1 : val_ - 1; return *this; }
	constexpr ModInt & operator +=(const ModInt & rhs) noexcept { val_ += val_ < M - rhs.val_ ? rhs.val_ : rhs.val_ - M; return *this; }
	constexpr ModInt & operator -=(const ModInt & rhs) noexcept { val_ += val_ >= rhs.val_ ? -rhs.val_ : M - rhs.val_; return *this; }
	constexpr ModInt & operator *=(const ModInt & rhs) noexcept { val_ = static_cast<calc_type>(val_) * rhs.val_ % M; return *this; }
	constexpr ModInt & operator /=(const ModInt & rhs) noexcept { return *this *= rhs.inv(); }
	friend constexpr ModInt operator +(const ModInt & lhs, const ModInt & rhs) noexcept { return ModInt(lhs) += rhs; }
	friend constexpr ModInt operator -(const ModInt & lhs, const ModInt & rhs) noexcept { return ModInt(lhs) -= rhs; }
	friend constexpr ModInt operator *(const ModInt & lhs, const ModInt & rhs) noexcept { return ModInt(lhs) *= rhs; }
	friend constexpr ModInt operator /(const ModInt & lhs, const ModInt & rhs) noexcept { return ModInt(lhs) /= rhs; }
	friend constexpr bool operator ==(const ModInt & lhs, const ModInt & rhs) noexcept { return lhs.val_ == rhs.val_; }
	friend constexpr bool operator !=(const ModInt & lhs, const ModInt & rhs) noexcept { return !(lhs == rhs); }
	friend std::ostream & operator <<(std::ostream & os, const ModInt & rhs) { return os << rhs.val_; }
	friend std::istream & operator >>(std::istream & is, ModInt & rhs) { calc_type x; is >> x; rhs = ModInt(x); return is; }
	
	constexpr ModInt pow(calc_type n) const noexcept {
		ModInt res = 1, x = val_;
		if (n < 0) { x = x.inv(); n = -n; }
		while (n) { if (n & 1) res *= x; x *= x; n >>= 1; }
		return res;
	}
	
	constexpr ModInt inv() const noexcept {
		value_type a = val_, a1 = 1, a2 = 0, b = M, b1 = 0, b2 = 1;
		while (b > 0) {
			value_type q = a / b, r = a % b;
			value_type nb1 = a1 - q * b1, nb2 = a2 - q * b2;
			a = b; b = r;
			a1 = b1; b1 = nb1;
			a2 = b2; b2 = nb2;
		}
		assert(a == 1);
		return a1;
	}
};
using mint = ModInt<MOD>;

std::vector<std::pair<int, int>> fast_prime_factorization(int n, const std::vector<int> & smallest_prime_factor) {
	assert(n >= 0);
	assert(n <= smallest_prime_factor.size());
	std::vector<std::pair<int, int>> res;
	for (; n > 1; n /= smallest_prime_factor[n]) {
		if (res.empty() || res.back().first != smallest_prime_factor[n]) res.emplace_back(smallest_prime_factor[n], 1);
		else ++res.back().second;
	}
	return res;
}

std::vector<int> sieve_smallest_prime_factor(int n) {
	assert(n >= 0);
	std::vector<int> res(n + 1);
	std::iota(begin(res), end(res), 0);
	
	for (int i = 2; i * i <= n; ++i) {
		if (res[i] < i) continue;
		for (int j = i * i; j <= n; j += i) {
			if (res[j] == j) res[j] = i;
		}
	}
	
	return res;
}

int main() {
	int N;
	cin >> N;
	
	auto spf = sieve_smallest_prime_factor(N);
	
	bool first = true;
	map<int, int> mm;
	for (int i = N; i >= 2; --i) {
		auto pf = fast_prime_factorization(i, spf);
		if (pf.front().first == i && first) first = false;
		else {
			for (auto [p, c] : pf) if (mm[p] < c) mm[p] = c;
		}
	}
	mint ans = 1;
	for (auto [p, c] : mm) REP(i, c) ans *= p;
	cout << ans << endl;
}
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