test/verify/aoj-dpl-5-g.test.cpp

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• Last update: 2026-08-10 10:46:05+00:00
• Problem: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DPL_5_G

Depends on

• Bell Number (ベル数) (math/combinatorics/bell-number.hpp)
• Enumeration (組み合わせ) (math/combinatorics/enumeration.hpp)
• Montgomery Mod Int (math/combinatorics/montgomery-mod-int.hpp)

Code

// clang-format off
// competitive-verifier: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DPL_5_G
// clang-format on

#include <iostream>

#include "../../math/combinatorics/bell-number.hpp"
#include "../../math/combinatorics/montgomery-mod-int.hpp"

using namespace std;

int main() {
  int N, K;
  cin >> N >> K;
  cout << bell_number<modint1000000007>(N, K) << endl;
}

#line 1 "test/verify/aoj-dpl-5-g.test.cpp"
// clang-format off
// competitive-verifier: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DPL_5_G
// clang-format on

#include <iostream>

#line 2 "math/combinatorics/bell-number.hpp"

#include <algorithm>
#include <vector>

#line 2 "math/combinatorics/enumeration.hpp"

#line 4 "math/combinatorics/enumeration.hpp"
#include <cstddef>
#line 6 "math/combinatorics/enumeration.hpp"

/**
 * @brief Enumeration(組み合わせ)
 */
template <typename T>
struct Enumeration {
 private:
  static std::vector<T> _fact, _finv, _inv;

  inline static void expand(std::size_t sz) {
    if (_fact.size() < sz + 1) {
      int pre_sz = std::max(1, (int)_fact.size());
      _fact.resize(sz + 1, T(1));
      _finv.resize(sz + 1, T(1));
      _inv.resize(sz + 1, T(1));
      for (int i = pre_sz; i <= (int)sz; i++) {
        _fact[i] = _fact[i - 1] * T(i);
      }
      _finv[sz] = T(1) / _fact[sz];
      for (int i = (int)sz - 1; i >= pre_sz; i--) {
        _finv[i] = _finv[i + 1] * T(i + 1);
      }
      for (int i = pre_sz; i <= (int)sz; i++) {
        _inv[i] = _finv[i] * _fact[i - 1];
      }
    }
  }

 public:
  explicit Enumeration(std::size_t sz = 0) { expand(sz); }

  static inline T fact(int k) {
    expand(k);
    return _fact[k];
  }

  static inline T finv(int k) {
    expand(k);
    return _finv[k];
  }

  static inline T inv(int k) {
    expand(k);
    return _inv[k];
  }

  static T P(int n, int r) {
    if (r < 0 || n < r) return 0;
    return fact(n) * finv(n - r);
  }

  static T C(int p, int q) {
    if (q < 0 || p < q) return 0;
    return fact(p) * finv(q) * finv(p - q);
  }

  static T H(int n, int r) {
    if (n < 0 || r < 0) return 0;
    return r == 0 ? 1 : C(n + r - 1, r);
  }
};

template <typename T>
std::vector<T> Enumeration<T>::_fact = std::vector<T>();
template <typename T>
std::vector<T> Enumeration<T>::_finv = std::vector<T>();
template <typename T>
std::vector<T> Enumeration<T>::_inv = std::vector<T>();
#line 7 "math/combinatorics/bell-number.hpp"

/**
 * @brief Bell Number(ベル数)
 *
 */
template <typename T>
T bell_number(int n, int k) {
  if (n == 0) return 1;
  k = std::min(k, n);
  Enumeration<T> uku(k);
  T ret = 0;
  std::vector<T> pref(k + 1);
  pref[0] = 1;
  for (int i = 1; i <= k; i++) {
    if (i & 1)
      pref[i] = pref[i - 1] - uku.finv(i);
    else
      pref[i] = pref[i - 1] + uku.finv(i);
  }
  for (int i = 1; i <= k; i++) {
    ret += T(i).pow(n) * uku.finv(i) * pref[k - i];
  }
  return ret;
}
#line 2 "math/combinatorics/montgomery-mod-int.hpp"

#include <cstdint>
#line 5 "math/combinatorics/montgomery-mod-int.hpp"

template <std::uint32_t mod_, bool fast = false>
struct MontgomeryModInt {
 private:
  using mint = MontgomeryModInt;
  using i32 = std::int32_t;
  using i64 = std::int64_t;
  using u32 = std::uint32_t;
  using u64 = std::uint64_t;

  static constexpr u32 get_r() {
    u32 ret = mod_;
    for (i32 i = 0; i < 4; i++) ret *= 2 - mod_ * ret;
    return ret;
  }

  static constexpr u32 r = get_r();

  static constexpr u32 n2 = -u64(mod_) % mod_;

  static_assert(r * mod_ == 1, "invalid, r * mod != 1");
  static_assert(mod_ < (1 << 30), "invalid, mod >= 2 ^ 30");
  static_assert((mod_ & 1) == 1, "invalid, mod % 2 == 0");

  u32 x;

 public:
  MontgomeryModInt() : x{} {}

  MontgomeryModInt(const i64& a)
      : x(reduce(u64(fast ? a : (a % mod() + mod())) * n2)) {}

  static constexpr u32 reduce(const u64& b) {
    return u32(b >> 32) + mod() - u32((u64(u32(b) * r) * mod()) >> 32);
  }

  mint& operator+=(const mint& p) {
    if (i32(x += p.x - 2 * mod()) < 0) x += 2 * mod();
    return *this;
  }

  mint& operator-=(const mint& p) {
    if (i32(x -= p.x) < 0) x += 2 * mod();
    return *this;
  }

  mint& operator*=(const mint& p) {
    x = reduce(u64(x) * p.x);
    return *this;
  }

  mint& operator/=(const mint& p) {
    *this *= p.inv();
    return *this;
  }

  mint operator-() const { return mint() - *this; }

  mint operator+(const mint& p) const { return mint(*this) += p; }

  mint operator-(const mint& p) const { return mint(*this) -= p; }

  mint operator*(const mint& p) const { return mint(*this) *= p; }

  mint operator/(const mint& p) const { return mint(*this) /= p; }

  bool operator==(const mint& p) const {
    return (x >= mod() ? x - mod() : x) == (p.x >= mod() ? p.x - mod() : p.x);
  }

  bool operator!=(const mint& p) const {
    return (x >= mod() ? x - mod() : x) != (p.x >= mod() ? p.x - mod() : p.x);
  }

  u32 val() const {
    u32 ret = reduce(x);
    return ret >= mod() ? ret - mod() : ret;
  }

  mint pow(u64 n) const {
    mint ret(1), mul(*this);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  mint inv() const { return pow(mod() - 2); }

  friend std::ostream& operator<<(std::ostream& os, const mint& p) {
    return os << p.val();
  }

  friend std::istream& operator>>(std::istream& is, mint& a) {
    i64 t;
    is >> t;
    a = mint(t);
    return is;
  }

  static constexpr u32 mod() { return mod_; }
};

template <std::uint32_t mod>
using modint = MontgomeryModInt<mod>;
using modint998244353 = modint<998244353>;
using modint1000000007 = modint<1000000007>;
#line 9 "test/verify/aoj-dpl-5-g.test.cpp"

using namespace std;

int main() {
  int N, K;
  cin >> N >> K;
  cout << bell_number<modint1000000007>(N, K) << endl;
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	00_sample_01	AC	2 ms	4 MB
g++	00_sample_02	AC	2 ms	4 MB
g++	00_sample_03	AC	2 ms	4 MB
g++	01_corner_00	AC	2 ms	4 MB
g++	01_corner_01	AC	2 ms	4 MB
g++	01_corner_02	AC	2 ms	4 MB
g++	02_maximum_00	AC	2 ms	4 MB
g++	02_maximum_01	AC	2 ms	4 MB
g++	03_random_00	AC	2 ms	4 MB
g++	03_random_01	AC	2 ms	4 MB
g++	03_random_02	AC	2 ms	4 MB
g++	03_random_03	AC	2 ms	4 MB
g++	03_random_04	AC	2 ms	4 MB
g++	03_random_05	AC	2 ms	4 MB
g++	03_random_06	AC	2 ms	4 MB
g++	03_random_07	AC	2 ms	4 MB
g++	03_random_08	AC	2 ms	4 MB
g++	03_random_09	AC	2 ms	4 MB
g++	03_random_10	AC	2 ms	4 MB
g++	03_random_11	AC	2 ms	4 MB
g++	03_random_12	AC	2 ms	4 MB
g++	03_random_13	AC	2 ms	4 MB
g++	03_random_14	AC	2 ms	4 MB
g++	03_random_15	AC	2 ms	4 MB
g++	03_random_16	AC	2 ms	4 MB
g++	03_random_17	AC	2 ms	4 MB
g++	03_random_18	AC	2 ms	4 MB
g++	03_random_19	AC	2 ms	4 MB
clang++	00_sample_01	AC	2 ms	4 MB
clang++	00_sample_02	AC	2 ms	4 MB
clang++	00_sample_03	AC	2 ms	4 MB
clang++	01_corner_00	AC	2 ms	4 MB
clang++	01_corner_01	AC	1 ms	4 MB
clang++	01_corner_02	AC	2 ms	4 MB
clang++	02_maximum_00	AC	2 ms	4 MB
clang++	02_maximum_01	AC	2 ms	4 MB
clang++	03_random_00	AC	1 ms	4 MB
clang++	03_random_01	AC	1 ms	4 MB
clang++	03_random_02	AC	2 ms	4 MB
clang++	03_random_03	AC	2 ms	4 MB
clang++	03_random_04	AC	1 ms	4 MB
clang++	03_random_05	AC	2 ms	4 MB
clang++	03_random_06	AC	2 ms	4 MB
clang++	03_random_07	AC	2 ms	4 MB
clang++	03_random_08	AC	2 ms	4 MB
clang++	03_random_09	AC	2 ms	4 MB
clang++	03_random_10	AC	2 ms	4 MB
clang++	03_random_11	AC	2 ms	4 MB
clang++	03_random_12	AC	2 ms	4 MB
clang++	03_random_13	AC	1 ms	4 MB
clang++	03_random_14	AC	1 ms	4 MB
clang++	03_random_15	AC	1 ms	4 MB
clang++	03_random_16	AC	2 ms	4 MB
clang++	03_random_17	AC	2 ms	4 MB
clang++	03_random_18	AC	1 ms	4 MB
clang++	03_random_19	AC	2 ms	4 MB

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