#937709 (C++23) No.2582 Random Average^K

• 問題: No.2582 Random Average^K
• ユーザー: 👑 emthrm
• 提出日時: 2023-12-10 00:45:54
• 言語: C++23 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 260 ms / 2,000 ms
• コード長: 5,515 bytes
• コンパイル時間: 3,247 ms
• コンパイル使用メモリ: 250,008 KB
• 実行使用メモリ: 89,172 KB
• 最終ジャッジ日時: 2024-09-27 03:56:08
• 合計ジャッジ時間: 5,058 ms
• ジャッジサーバーID （参考情報）: judge4 / judge3

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	1 ms; 5,248 KB
testcase_01	AC	2 ms; 5,376 KB
testcase_02	AC	2 ms; 5,376 KB
testcase_03	AC	2 ms; 5,376 KB
testcase_04	AC	2 ms; 5,376 KB
testcase_05	AC	2 ms; 5,376 KB
testcase_06	AC	2 ms; 5,376 KB
testcase_07	AC	1 ms; 5,376 KB
testcase_08	AC	3 ms; 5,376 KB
testcase_09	AC	67 ms; 28,940 KB
testcase_10	AC	155 ms; 68,020 KB
testcase_11	AC	125 ms; 51,704 KB
testcase_12	AC	260 ms; 89,172 KB
testcase_13	AC	119 ms; 10,976 KB
testcase_14	AC	130 ms; 81,196 KB
testcase_15	AC	260 ms; 88,816 KB
testcase_16	AC	209 ms; 85,504 KB
testcase_17	AC	212 ms; 85,376 KB

ソースコード

#include <bits/stdc++.h>
using namespace std;
#define FOR(i,m,n) for(int i=(m);i<(n);++i)
#define REP(i,n) FOR(i,0,n)
using ll = long long;
constexpr int INF = 0x3f3f3f3f;
constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL;
constexpr double EPS = 1e-8;
constexpr int MOD = 998244353;
// constexpr int MOD = 1000000007;
constexpr int DY4[]{1, 0, -1, 0}, DX4[]{0, -1, 0, 1};
constexpr int DY8[]{1, 1, 0, -1, -1, -1, 0, 1};
constexpr int DX8[]{0, -1, -1, -1, 0, 1, 1, 1};
template <typename T, typename U>
inline bool chmax(T& a, U b) { return a < b ? (a = b, true) : false; }
template <typename T, typename U>
inline bool chmin(T& a, U b) { return a > b ? (a = b, true) : false; }
struct IOSetup {
  IOSetup() {
    std::cin.tie(nullptr);
    std::ios_base::sync_with_stdio(false);
    std::cout << fixed << setprecision(20);
  }
} iosetup;

template <unsigned int M>
struct MInt {
  unsigned int v;

  constexpr MInt() : v(0) {}
  constexpr MInt(const long long x) : v(x >= 0 ? x % M : x % M + M) {}
  static constexpr MInt raw(const int x) {
    MInt x_;
    x_.v = x;
    return x_;
  }

  static constexpr int get_mod() { return M; }
  static constexpr void set_mod(const int divisor) {
    assert(std::cmp_equal(divisor, M));
  }

  static void init(const int x) {
    inv<true>(x);
    fact(x);
    fact_inv(x);
  }

  template <bool MEMOIZES = false>
  static MInt inv(const int n) {
    // assert(0 <= n && n < M && std::gcd(n, M) == 1);
    static std::vector<MInt> inverse{0, 1};
    const int prev = inverse.size();
    if (n < prev) return inverse[n];
    if constexpr (MEMOIZES) {
      // "n!" and "M" must be disjoint.
      inverse.resize(n + 1);
      for (int i = prev; i <= n; ++i) {
        inverse[i] = -inverse[M % i] * raw(M / i);
      }
      return inverse[n];
    }
    int u = 1, v = 0;
    for (unsigned int a = n, b = M; b;) {
      const unsigned int q = a / b;
      std::swap(a -= q * b, b);
      std::swap(u -= q * v, v);
    }
    return u;
  }

  static MInt fact(const int n) {
    static std::vector<MInt> factorial{1};
    if (const int prev = factorial.size(); n >= prev) {
      factorial.resize(n + 1);
      for (int i = prev; i <= n; ++i) {
        factorial[i] = factorial[i - 1] * i;
      }
    }
    return factorial[n];
  }

  static MInt fact_inv(const int n) {
    static std::vector<MInt> f_inv{1};
    if (const int prev = f_inv.size(); n >= prev) {
      f_inv.resize(n + 1);
      f_inv[n] = inv(fact(n).v);
      for (int i = n; i > prev; --i) {
        f_inv[i - 1] = f_inv[i] * i;
      }
    }
    return f_inv[n];
  }

  static MInt nCk(const int n, const int k) {
    if (n < 0 || n < k || k < 0) [[unlikely]] return MInt();
    return fact(n) * (n - k < k ? fact_inv(k) * fact_inv(n - k) :
                                  fact_inv(n - k) * fact_inv(k));
  }
  static MInt nPk(const int n, const int k) {
    return n < 0 || n < k || k < 0 ? MInt() : fact(n) * fact_inv(n - k);
  }
  static MInt nHk(const int n, const int k) {
    return n < 0 || k < 0 ? MInt() : (k == 0 ? 1 : nCk(n + k - 1, k));
  }

  static MInt large_nCk(long long n, const int k) {
    if (n < 0 || n < k || k < 0) [[unlikely]] return MInt();
    inv<true>(k);
    MInt res = 1;
    for (int i = 1; i <= k; ++i) {
      res *= inv(i) * n--;
    }
    return res;
  }

  constexpr MInt pow(long long exponent) const {
    MInt res = 1, tmp = *this;
    for (; exponent > 0; exponent >>= 1) {
      if (exponent & 1) res *= tmp;
      tmp *= tmp;
    }
    return res;
  }

  constexpr MInt& operator+=(const MInt& x) {
    if ((v += x.v) >= M) v -= M;
    return *this;
  }
  constexpr MInt& operator-=(const MInt& x) {
    if ((v += M - x.v) >= M) v -= M;
    return *this;
  }
  constexpr MInt& operator*=(const MInt& x) {
    v = (unsigned long long){v} * x.v % M;
    return *this;
  }
  MInt& operator/=(const MInt& x) { return *this *= inv(x.v); }

  constexpr auto operator<=>(const MInt& x) const = default;

  constexpr MInt& operator++() {
    if (++v == M) [[unlikely]] v = 0;
    return *this;
  }
  constexpr MInt operator++(int) {
    const MInt res = *this;
    ++*this;
    return res;
  }
  constexpr MInt& operator--() {
    v = (v == 0 ? M - 1 : v - 1);
    return *this;
  }
  constexpr MInt operator--(int) {
    const MInt res = *this;
    --*this;
    return res;
  }

  constexpr MInt operator+() const { return *this; }
  constexpr MInt operator-() const { return raw(v ? M - v : 0); }

  constexpr MInt operator+(const MInt& x) const { return MInt(*this) += x; }
  constexpr MInt operator-(const MInt& x) const { return MInt(*this) -= x; }
  constexpr MInt operator*(const MInt& x) const { return MInt(*this) *= x; }
  MInt operator/(const MInt& x) const { return MInt(*this) /= x; }

  friend std::ostream& operator<<(std::ostream& os, const MInt& x) {
    return os << x.v;
  }
  friend std::istream& operator>>(std::istream& is, MInt& x) {
    long long v;
    is >> v;
    x = MInt(v);
    return is;
  }
};
using ModInt = MInt<MOD>;

//   [x^K] ((e^x - 1) / x)^N
// = [x^(K + N)] (e^x - 1)^N
// = [x^(K + N)] \sum_{i = 0}^N \binom{N}{i} e^(ix) (-1)^(N - i)
// = \sum_{i = 0}^N \binom{N}{i} (-1)^(N - i) [x^(K + N)] e^(ix)
// = \sum_{i = 0}^N \binom{N}{i} (-1)^(N - i) i^(K + N) / (K + N)!
int main() {
  int n, k; cin >> n >> k;
  ModInt ans = 0;
  REP(i, n + 1) ans += ModInt::nCk(n, i) * ((n - i) % 2 == 0 ? 1 : -1) * ModInt::raw(i).pow(k + n) * ModInt::fact_inv(k + n);
  cout << ans * ModInt::fact(k) / ModInt::raw(n).pow(k) << '\n';
  return 0;
}