#820076 (C++17) No.2130 分配方法の数え上げ mod 998244353

• 問題: No.2130 分配方法の数え上げ mod 998244353
• ユーザー: 👑 emthrm
• 提出日時: 2022-11-26 03:31:19
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 4 ms / 2,000 ms
• コード長: 4,855 bytes
• コンパイル時間: 728 ms
• コンパイル使用メモリ: 80,684 KB
• 実行使用メモリ: 6,820 KB
• 最終ジャッジ日時: 2024-10-02 08:40:32
• 合計ジャッジ時間: 1,913 ms
• ジャッジサーバーID （参考情報）: judge1 / judge5

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 6,816 KB
testcase_01	AC	2 ms; 6,816 KB
testcase_02	AC	2 ms; 6,820 KB
testcase_03	AC	2 ms; 6,816 KB
testcase_04	AC	2 ms; 6,820 KB
testcase_05	AC	2 ms; 6,820 KB
testcase_06	AC	1 ms; 6,820 KB
testcase_07	AC	2 ms; 6,816 KB
testcase_08	AC	2 ms; 6,816 KB
testcase_09	AC	2 ms; 6,816 KB
testcase_10	AC	2 ms; 6,816 KB
testcase_11	AC	2 ms; 6,816 KB
testcase_12	AC	2 ms; 6,820 KB
testcase_13	AC	2 ms; 6,820 KB
testcase_14	AC	2 ms; 6,816 KB
testcase_15	AC	2 ms; 6,816 KB
testcase_16	AC	2 ms; 6,820 KB
testcase_17	AC	2 ms; 6,816 KB
testcase_18	AC	2 ms; 6,820 KB
testcase_19	AC	2 ms; 6,816 KB
testcase_20	AC	2 ms; 6,820 KB
testcase_21	AC	2 ms; 6,816 KB
testcase_22	AC	2 ms; 6,816 KB
testcase_23	AC	2 ms; 6,816 KB
testcase_24	AC	2 ms; 6,816 KB
testcase_25	AC	2 ms; 6,816 KB
testcase_26	AC	2 ms; 6,820 KB
testcase_27	AC	4 ms; 6,820 KB
testcase_28	AC	2 ms; 6,820 KB
testcase_29	AC	4 ms; 6,816 KB
testcase_30	AC	2 ms; 6,820 KB
testcase_31	AC	2 ms; 6,816 KB
testcase_32	AC	2 ms; 6,816 KB
testcase_33	AC	2 ms; 6,820 KB
testcase_34	AC	2 ms; 6,820 KB
testcase_35	AC	2 ms; 6,816 KB
testcase_36	AC	2 ms; 6,816 KB
testcase_37	AC	2 ms; 6,820 KB

ソースコード

#include <algorithm>
#include <cassert>
#include <iostream>
#include <numeric>
#include <utility>
#include <vector>

template <int M>
struct MInt {
  unsigned int v;
  MInt() : v(0) {}
  MInt(const long long x) : v(x >= 0 ? x % M : x % M + M) {}
  static constexpr int get_mod() { return M; }
  static void set_mod(const int divisor) { assert(divisor == M); }
  static void init(const int x = 10000000) {
    inv(x, true);
    fact(x);
    fact_inv(x);
  }
  static MInt inv(const int n, const bool init = false) {
    // 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];
    } else if (init) {
      // "n!" and "M" must be disjoint.
      inverse.resize(n + 1);
      for (int i = prev; i <= n; ++i) {
        inverse[i] = -inverse[M % i] * (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};
    const int prev = factorial.size();
    if (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};
    const int prev = f_inv.size();
    if (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) return 0;
    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 ? 0 : fact(n) * fact_inv(n - k);
  }
  static MInt nHk(const int n, const int k) {
    return n < 0 || k < 0 ? 0 : (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) return 0;
    inv(k, true);
    MInt res = 1;
    for (int i = 1; i <= k; ++i) {
      res *= inv(i) * n--;
    }
    return res;
  }
  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;
  }
  MInt& operator+=(const MInt& x) {
    if ((v += x.v) >= M) v -= M;
    return *this;
  }
  MInt& operator-=(const MInt& x) {
    if ((v += M - x.v) >= M) v -= M;
    return *this;
  }
  MInt& operator*=(const MInt& x) {
    v = static_cast<unsigned long long>(v) * x.v % M;
    return *this;
  }
  MInt& operator/=(const MInt& x) { return *this *= inv(x.v); }
  bool operator==(const MInt& x) const { return v == x.v; }
  bool operator!=(const MInt& x) const { return v != x.v; }
  bool operator<(const MInt& x) const { return v < x.v; }
  bool operator<=(const MInt& x) const { return v <= x.v; }
  bool operator>(const MInt& x) const { return v > x.v; }
  bool operator>=(const MInt& x) const { return v >= x.v; }
  MInt& operator++() {
    if (++v == M) v = 0;
    return *this;
  }
  MInt operator++(int) {
    const MInt res = *this;
    ++*this;
    return res;
  }
  MInt& operator--() {
    v = (v == 0 ? M - 1 : v - 1);
    return *this;
  }
  MInt operator--(int) {
    const MInt res = *this;
    --*this;
    return res;
  }
  MInt operator+() const { return *this; }
  MInt operator-() const { return MInt(v ? M - v : 0); }
  MInt operator+(const MInt& x) const { return MInt(*this) += x; }
  MInt operator-(const MInt& x) const { return MInt(*this) -= x; }
  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;
  }
};

template <int T>
std::vector<MInt<T>> large_nCk_init(long long n, const int k) {
  using ModInt = MInt<T>;
  const int tmp = std::min(n, static_cast<long long>(k));
  ModInt::inv(tmp, true);
  std::vector<ModInt> c(k + 1, 0);
  c.front() = 1;
  for (int i = 1; i <= tmp; ++i) {
    c[i] = c[i - 1] * n-- * ModInt::inv(i);
  }
  return c;
}

int main() {
  constexpr int MOD = 998244353;
  using ModInt = MInt<MOD>;
  long long n;
  int m;
  std::cin >> n >> m;
  const std::vector<ModInt> c = large_nCk_init<MOD>(n, m - 1);
  std::cout << ModInt(2).pow(n) - std::accumulate(c.begin(), c.end(), ModInt(0))
            << '\n';
  return 0;
}