#618187 (C++17) No.1396 Giri

• 問題: No.1396 Giri
• ユーザー: kcvlex
• 提出日時: 2021-02-14 21:46:43
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 13 ms / 2,000 ms
• コード長: 7,519 bytes
• コンパイル時間: 1,458 ms
• コンパイル使用メモリ: 153,168 KB
• 最終ジャッジ日時: 2025-01-18 20:52:27
• ジャッジサーバーID （参考情報）: judge5 / judge2

ファイルパターン	結果
sample	AC * 3
other	AC * 23

ソースコード

#include <limits>
#include <initializer_list>
#include <utility>
#include <bitset>
#include <tuple>
#include <type_traits>
#include <functional>
#include <string>
#include <array>
#include <deque>
#include <list>
#include <queue>
#include <stack>
#include <vector>
#include <map>
#include <set>
#include <unordered_map>
#include <unordered_set>
#include <iterator>
#include <algorithm>
#include <complex>
#include <random>
#include <numeric>
#include <iostream>
#include <iomanip>
#include <sstream>
#include <regex>
#include <cassert>
#include <cstddef>
#include <variant>

#define endl codeforces

#define ALL(v) std::begin(v), std::end(v)
#define ALLR(v) std::rbegin(v), std::rend(v)

using ll = std::int64_t;
using ull = std::uint64_t;
using pii = std::pair<int, int>;
using tii = std::tuple<int, int, int>;
using pll = std::pair<ll, ll>;
using tll = std::tuple<ll, ll, ll>;
using size_type = ssize_t;
template <typename T> using vec = std::vector<T>;
template <typename T> using vvec = vec<vec<T>>;

template <typename T> const T& var_min(const T &t) { return t; }
template <typename T> const T& var_max(const T &t) { return t; }
template <typename T, typename... Tail> const T& var_min(const T &t, const Tail&... tail) { return std::min(t, var_min(tail...)); }
template <typename T, typename... Tail> const T& var_max(const T &t, const Tail&... tail) { return std::max(t, var_max(tail...)); }
template <typename T, typename... Tail> void chmin(T &t, const Tail&... tail) { t = var_min(t, tail...); }
template <typename T, typename... Tail> void chmax(T &t, const Tail&... tail) { t = var_max(t, tail...); }

template <typename T, std::size_t Head, std::size_t... Tail> 
struct multi_dim_array { using type = std::array<typename multi_dim_array<T, Tail...>::type, Head>; };

template <typename T, std::size_t Head> 
struct multi_dim_array<T, Head> { using type = std::array<T, Head>; };

template <typename T, std::size_t... Args> using mdarray = typename multi_dim_array<T, Args...>::type;

template <typename T, typename F, typename... Args> 
void fill_seq(T &t, F f, Args... args) { 
    if constexpr (std::is_invocable<F, Args...>::value) { 
        t = f(args...); 
    } else { 
        for (size_type i = 0; i < t.size(); i++) fill_seq(t[i], f, args..., i); 
    } 
}

template <typename T> vec<T> make_v(size_type sz) { return vec<T>(sz); }

template <typename T, typename... Tail> 
auto make_v(size_type hs, Tail&&... ts) { 
    auto v = std::move(make_v<T>(std::forward<Tail>(ts)...)); 
    return vec<decltype(v)>(hs, v); 
}

namespace init__ { 
struct InitIO { 
    InitIO() { 
        std::cin.tie(nullptr); 
        std::ios_base::sync_with_stdio(false); 
        std::cout << std::fixed << std::setprecision(30); 
    } 
} init_io; 
}

template <typename T>
T ceil_pow2(T bound) {
    T ret = 1;
    while (ret < bound) ret *= 2;
    return ret;
}

template <typename T>
T ceil_div(T a, T b) { return a / b + !!(a % b); }


namespace math {

// return the value \in [0, Mod)
// Rust's rem_euclid
constexpr std::uint64_t rem_euclid(const ll v, std::uint64_t Mod) {
    if (0 <= v) {
        return v % Mod;
    } else {
        const ll mod = static_cast<ll>(Mod);
        return static_cast<std::uint64_t>(Mod + v % Mod) % Mod;
    }
}

template <typename T>
constexpr T mul_id_ele() {
    if constexpr (std::is_fundamental<T>::value) {
        return T(1);
    } else {
        return T::mul_id_ele();
    }
}

template <typename T>
constexpr T add_id_ele() {
    if constexpr (std::is_fundamental<T>::value) {
        return T(0);
    } else {
        return T::add_id_ele();
    }
}

template <typename T>
constexpr T pow(const T &n, ll k) {
    T ret = mul_id_ele<T>();
    T cur = n;
    while (k) {
        if (k & 1) ret *= cur;
        cur *= cur;
        k /= 2;
    }
    return ret;
}

template <typename T>
typename std::enable_if<std::is_integral<T>::value, T>::type
gcd(T a, T b) { return b ? gcd(a % b, b) : a; }

}

namespace math {

// Mod * 2 must be less than std::numeric_limits<std::uint32_t>::max()
template <std::uint32_t Mod>
struct Modint {
    using value_type = std::uint32_t;

    constexpr Modint() noexcept : Modint(0) { }

    constexpr Modint(ll x) noexcept
        : x(static_cast<value_type>(rem_euclid(x, Mod)))
    {
    }
    
    constexpr static Modint add_id_ele() { 
        return Modint(0); 
    }
    
    constexpr static Modint mul_id_ele() {
        return Modint(1u);
    }
    
    constexpr value_type value() const noexcept { 
        return x;
    }

    constexpr Modint& operator+=(const Modint &oth) noexcept {
        x += oth.value();
        if (Mod <= x) x -= Mod;
        return *this;
    }

    constexpr Modint& operator-=(const Modint &oth) noexcept {
        x += Mod - oth.value();
        if (Mod <= x) x -= Mod;
        return *this;
    }

    constexpr Modint& operator*=(const Modint &oth) noexcept {
        std::uint64_t v = x;
        v *= oth.value();
        x = static_cast<value_type>(v % Mod);
        return *this;
    }

    constexpr Modint& operator/=(const Modint &oth) noexcept {
        return (*this) *= oth.inv();
    }

    constexpr Modint& operator++() noexcept {
        x++;
        if (x == Mod) x = 0;
        return *this;
    }

    constexpr Modint& operator--() noexcept {
        if (x == 0) x = Mod - 1;
        else x--;
        return *this;
    }

    constexpr Modint operator+(const Modint &oth) const noexcept { return Modint(x) += oth; }
    constexpr Modint operator-(const Modint &oth) const noexcept { return Modint(x) -= oth; }
    constexpr Modint operator*(const Modint &oth) const noexcept { return Modint(x) *= oth; }
    constexpr Modint operator/(const Modint &oth) const noexcept { return Modint(x) /= oth; }
    constexpr Modint operator-() const noexcept { return Modint((x != 0) * (Mod - x)); }
    constexpr Modint operator++() const noexcept { return Modint(x + 1); }
    constexpr Modint operator--() const noexcept { return Modint(x ? x - 1 : Mod - 1); }
    constexpr bool operator==(const Modint &oth) const noexcept { return value() == oth.value(); }
    constexpr bool operator!=(const Modint &oth) const noexcept { return !(*this == oth); }

    template <typename T>
    constexpr typename std::enable_if<std::is_integral<T>::value, const Modint&>::type
    operator=(T t) noexcept {
        (*this) = Modint(std::forward<T>(t)); 
        return *this;
    }

    constexpr Modint inv() const noexcept {
        return ::math::pow(*this, Mod - 2);
    }

    constexpr value_type mod() const noexcept {
        return Mod;
    }

private:
    value_type x;
};

template <std::uint32_t Mod>
Modint<Mod> inv(Modint<Mod> m) {
    return m.inv();
}

template <std::uint32_t Mod>
std::istream& operator>>(std::istream &is, Modint<Mod> &m) {
    ll v;
    is >> v;
    m = v;
    return is;
}

template <std::uint32_t Mod>
std::ostream& operator<<(std::ostream &os, Modint<Mod> m) {
    os << m.value();
    return os;
}

}

constexpr ll mod = 998'244'353;
using mint = math::Modint<mod>;

int main() {
    ll n;
    std::cin >> n;
    vec<bool> used(n + 1);
    vec<ll> primes;
    for (ll i = 2; i <= n; i++) {
        if (used[i]) continue;
        primes.push_back(i);
        for (ll j = 1; i * j <= n; j++) used[i * j] = true;
    }

    mint ans = 1;
    ll maxv = 1;
    for (ll p : primes) {
        chmax(maxv, p);
        ll tmp = 1;
        while (tmp * p <= n) tmp *= p;
        ans *= tmp;
    }
    ans /= maxv;
    std::cout << ans << "\n";
    return 0;
}