#663221 (C++17) No.1529 Constant Lcm

• 問題: No.1529 Constant Lcm
• ユーザー: Haar
• 提出日時: 2021-06-04 20:20:10
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 383 ms / 3,000 ms
• コード長: 4,713 bytes
• コンパイル時間: 2,249 ms
• コンパイル使用メモリ: 204,968 KB
• 最終ジャッジ日時: 2025-01-21 21:53:09
• ジャッジサーバーID （参考情報）: judge5 / judge4

ファイルパターン	結果
sample	AC * 2
other	AC * 24

ソースコード

#include <bits/stdc++.h>

namespace haar_lib {
  template <int32_t M>
  class modint {
    uint32_t val_;

  public:
    constexpr static auto mod() { return M; }

    constexpr modint() : val_(0) {}
    constexpr modint(int64_t n) {
      if (n >= M)
        val_ = n % M;
      else if (n < 0)
        val_ = n % M + M;
      else
        val_ = n;
    }

    constexpr auto &operator=(const modint &a) {
      val_ = a.val_;
      return *this;
    }
    constexpr auto &operator+=(const modint &a) {
      if (val_ + a.val_ >= M)
        val_ = (uint64_t) val_ + a.val_ - M;
      else
        val_ += a.val_;
      return *this;
    }
    constexpr auto &operator-=(const modint &a) {
      if (val_ < a.val_) val_ += M;
      val_ -= a.val_;
      return *this;
    }
    constexpr auto &operator*=(const modint &a) {
      val_ = (uint64_t) val_ * a.val_ % M;
      return *this;
    }
    constexpr auto &operator/=(const modint &a) {
      val_ = (uint64_t) val_ * a.inv().val_ % M;
      return *this;
    }

    constexpr auto operator+(const modint &a) const { return modint(*this) += a; }
    constexpr auto operator-(const modint &a) const { return modint(*this) -= a; }
    constexpr auto operator*(const modint &a) const { return modint(*this) *= a; }
    constexpr auto operator/(const modint &a) const { return modint(*this) /= a; }

    constexpr bool operator==(const modint &a) const { return val_ == a.val_; }
    constexpr bool operator!=(const modint &a) const { return val_ != a.val_; }

    constexpr auto &operator++() {
      *this += 1;
      return *this;
    }
    constexpr auto &operator--() {
      *this -= 1;
      return *this;
    }

    constexpr auto operator++(int) {
      auto t = *this;
      *this += 1;
      return t;
    }
    constexpr auto operator--(int) {
      auto t = *this;
      *this -= 1;
      return t;
    }

    constexpr static modint pow(int64_t n, int64_t p) {
      if (p < 0) return pow(n, -p).inv();

      int64_t ret = 1, e = n % M;
      for (; p; (e *= e) %= M, p >>= 1)
        if (p & 1) (ret *= e) %= M;
      return ret;
    }

    constexpr static modint inv(int64_t a) {
      int64_t b = M, u = 1, v = 0;

      while (b) {
        int64_t t = a / b;
        a -= t * b;
        std::swap(a, b);
        u -= t * v;
        std::swap(u, v);
      }

      u %= M;
      if (u < 0) u += M;

      return u;
    }

    constexpr static auto frac(int64_t a, int64_t b) { return modint(a) / modint(b); }

    constexpr auto pow(int64_t p) const { return pow(val_, p); }
    constexpr auto inv() const { return inv(val_); }

    friend constexpr auto operator-(const modint &a) { return modint(M - a.val_); }

    friend constexpr auto operator+(int64_t a, const modint &b) { return modint(a) + b; }
    friend constexpr auto operator-(int64_t a, const modint &b) { return modint(a) - b; }
    friend constexpr auto operator*(int64_t a, const modint &b) { return modint(a) * b; }
    friend constexpr auto operator/(int64_t a, const modint &b) { return modint(a) / b; }

    friend std::istream &operator>>(std::istream &s, modint &a) {
      s >> a.val_;
      return s;
    }
    friend std::ostream &operator<<(std::ostream &s, const modint &a) {
      s << a.val_;
      return s;
    }

    template <int N>
    static auto div() {
      static auto value = inv(N);
      return value;
    }

    explicit operator int32_t() const noexcept { return val_; }
    explicit operator int64_t() const noexcept { return val_; }
  };
}  // namespace haar_lib




namespace haar_lib {
  class prime_factorize_sieve {
    std::vector<int> p_;

  public:
    prime_factorize_sieve() {}
    prime_factorize_sieve(int N) : p_(N + 1) {
      for (int i = 2; i <= N; ++i) {
        if (p_[i] != 0) continue;
        for (int j = i; j <= N; j += i) {
          if (p_[j] == 0) p_[j] = i;
        }
      }
    }

    std::vector<int64_t> factorize(int N) const {
      std::vector<int64_t> ret;

      while (N > 1) {
        ret.push_back(p_[N]);
        N /= p_[N];
      }

      return ret;
    }
  };
}  // namespace haar_lib

using namespace haar_lib;
using mint = modint<998244353>;

int main() {
  int N; std::cin >> N;

  prime_factorize_sieve f(N);

  std::vector<int> count(N + 1);

  for (int i = 1; i <= (N + 1) / 2; ++i) {
    std::unordered_map<int, int> t;
    {
      auto res = f.factorize(i);
      for (int p : res) t[p] += 1;
    }
    {
      auto res = f.factorize(N - i);
      for (int p : res) t[p] += 1;
    }

    for (auto [p, c] : t) {
      count[p] = std::max(count[p], c);
    }
  }

  mint ans = 1;
  for (int i = 1; i <= N; ++i) {
    ans *= mint::pow(i, count[i]);
  }

  std::cout << ans << "\n";

  return 0;
}