#937706 (C++17) No.2582 Random Average^K

• 問題: No.2582 Random Average^K
• ユーザー: noshi91
• 提出日時: 2023-12-10 00:41:40
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 448 ms / 2,000 ms
• コード長: 5,265 bytes
• コンパイル時間: 2,133 ms
• コンパイル使用メモリ: 209,120 KB
• 実行使用メモリ: 138,468 KB
• 最終ジャッジ日時: 2023-12-10 00:41:46
• 合計ジャッジ時間: 5,241 ms
• ジャッジサーバーID （参考情報）: judge12 / judge11

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 6,676 KB
testcase_01	AC	1 ms; 6,676 KB
testcase_02	AC	2 ms; 6,676 KB
testcase_03	AC	2 ms; 6,676 KB
testcase_04	AC	1 ms; 6,676 KB
testcase_05	AC	2 ms; 6,676 KB
testcase_06	AC	3 ms; 6,676 KB
testcase_07	AC	3 ms; 6,676 KB
testcase_08	AC	3 ms; 6,676 KB
testcase_09	AC	107 ms; 38,116 KB
testcase_10	AC	189 ms; 70,884 KB
testcase_11	AC	191 ms; 70,884 KB
testcase_12	AC	448 ms; 138,468 KB
testcase_13	AC	214 ms; 11,516 KB
testcase_14	AC	185 ms; 134,396 KB
testcase_15	AC	408 ms; 138,468 KB
testcase_16	AC	300 ms; 136,420 KB
testcase_17	AC	300 ms; 136,420 KB

ソースコード

//#define NDEBUG
#pragma warning(disable : 4146)

#include <bits/stdc++.h>

namespace n91 {

  using i32 = std::int32_t;
  using i64 = std::int64_t;
  using u32 = std::uint32_t;
  using u64 = std::uint64_t;
  using isize = std::ptrdiff_t;
  using usize = std::size_t;
  using f64 = double;

  struct rep {
    struct itr {
      usize i;
      constexpr itr(const usize i) noexcept : i(i) {}
      void operator++() noexcept { ++i; }
      constexpr usize operator*() const noexcept { return i; }
      constexpr bool operator!=(const itr x) const noexcept { return i != x.i; }
    };
    const itr f, l;
    constexpr rep(const usize f, const usize l) noexcept
      : f(std::min(f, l)), l(l) {}
    constexpr auto begin() const noexcept { return f; }
    constexpr auto end() const noexcept { return l; }
  };
  struct revrep {
    struct itr {
      usize i;
      constexpr itr(const usize i) noexcept : i(i) {}
      void operator++() noexcept { --i; }
      constexpr usize operator*() const noexcept { return i; }
      constexpr bool operator!=(const itr x) const noexcept { return i != x.i; }
    };
    const itr f, l;
    constexpr revrep(const usize f, const usize l) noexcept
      : f(l - 1), l(std::min(f, l) - 1) {}
    constexpr auto begin() const noexcept { return f; }
    constexpr auto end() const noexcept { return l; }
  };
  template <class T> auto md_vec(const usize n, const T& value) {
    return std::vector<T>(n, value);
  }
  template <class... Args> auto md_vec(const usize n, Args... args) {
    return std::vector<decltype(md_vec(args...))>(n, md_vec(args...));
  }
  template <class T> constexpr T difference(const T& a, const T& b) noexcept {
    return a < b ? b - a : a - b;
  }
  template <class T> void chmin(T& a, const T& b) noexcept {
    if (b < a)
      a = b;
  }
  template <class T> void chmax(T& a, const T& b) noexcept {
    if (a < b)
      a = b;
  }
  template <class F> class rec_lambda {
    F f;

  public:
    rec_lambda(F&& f_) : f(std::forward<F>(f_)) {}
    template <class... Args> auto operator()(Args &&... args) const {
      return f(*this, std::forward<Args>(args)...);
    }
  };
  template <class T> T scan() {
    T ret;
    std::cin >> ret;
    return ret;
  }
  constexpr char eoln = '\n';

  i64 floor_div(const i64 n, const i64 d) {
    assert(d != 0);
    return n / d - static_cast<i64>((n ^ d) < 0 && n % d != 0);
  }

  i64 ceil_div(const i64 n, const i64 d) {
    assert(d != 0);
    return n / d + static_cast<i64>((n ^ d) >= 0 && n % d != 0);
  }

#ifdef N91_LOCAL
#define OJ_LOCAL(a, b) b
#else
#define OJ_LOCAL(a, b) a
#endif

} // namespace n91

#include <algorithm>
#include <cassert>
#include <vector>

namespace noshi91 {

  template <class T> class mint_utility {
    static inline std::vector<T> fact_ = { T::raw(1) };
    static inline std::vector<T> inv_fact_ = { T::raw(1) };

    static void extend(const int n) {
      const int s = fact_.size();
      if (n >= s) {
        int t = s;
        while (n >= t)
          t = std::min(t * 2, T::mod());
        fact_.resize(t);
        inv_fact_.resize(t);
        for (int i = s; i < t; i++) {
          fact_[i] = fact_[i - 1] * T::raw(i);
        }
        inv_fact_.back() = T::raw(1) / fact_.back();
        for (int i = t - 1; i > s; i--) {
          inv_fact_[i - 1] = inv_fact_[i] * T::raw(i);
        }
      }
    }

  public:
    mint_utility() = delete;

    static T fact(const int n) {
      assert(0 <= n && n < T::mod());
      extend(n);
      return fact_[n];
    }

    static T inv_fact(const int n) {
      assert(0 <= n && n < T::mod());
      extend(n);
      return inv_fact_[n];
    }

    static T binom(const int n, const int r) {
      assert(0 <= n && n < T::mod());
      if (r < 0 || n < r) {
        return T::raw(0);
      }
      else {
        extend(n);
        return fact_[n] * inv_fact_[r] * inv_fact_[n - r];
      }
    }

    static T binom2(const int a, const int b) {
      assert(0 <= a && 0 <= b && a + b < T::mod());
      extend(a + b);
      return fact_[a + b] * inv_fact_[a] * inv_fact_[b];
    }

    static T homo(const int n, const int r) {
      assert(1 <= n);
      if (r < 0)
        return T::raw(0);
      assert(n + r - 1 < T::mod());
      extend(n + r - 1);
      return fact_[n + r - 1] * inv_fact_[n - 1] * inv_fact_[r];
    }

    static T perm(const int n, const int r) {
      assert(0 <= r && n < T::mod());
      if (n < r) {
        return T::raw(0);
      }
      else {
        extend(n);
        return fact_[n] * inv_fact_[n - r];
      }
    }
  };

} // namespace noshi91

#include <atcoder/modint>
using mint = atcoder::modint998244353;
using util = noshi91::mint_utility<mint>;

namespace n91 {

  void main_() {
    const usize n = scan<usize>();
    const usize k = scan<usize>();
    mint ans = 0;
    for (const usize i : rep(0, n + 1)) {
      ans += mint(-1).pow(n - i) * util::binom(n, i) * mint(i).pow(n + k);
    }
    ans *= util::inv_fact(n + k);
    ans *= util::fact(k);
    ans *= (1 / mint(n)).pow(k);
    std::cout << ans.val() << eoln;
  }

} // namespace n91

int main() {
  //*
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  //*/
  std::cout << std::fixed << std::setprecision(20);
  n91::main_();
  return 0;
}