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

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• Last update: 2024-04-24 02:34:04+09:00
• Problem: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DPL_5_I

Depends on

• Enumeration(組み合わせ) (math/combinatorics/enumeration.hpp)
• math/combinatorics/montgomery-mod-int.hpp
• Stirling Number Second(第2種スターリング数) (math/combinatorics/stirling-number-second.hpp)
• template/template.hpp

Code

// competitive-verifier: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DPL_5_I

#include "../../template/template.hpp"

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

#include "../../math/combinatorics/stirling-number-second.hpp"

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

#line 1 "test/verify/aoj-dpl-5-i.test.cpp"
// competitive-verifier: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DPL_5_I

#line 1 "template/template.hpp"
#include<bits/stdc++.h>

using namespace std;

using int64 = long long;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;

template< typename T1, typename T2 >
ostream &operator<<(ostream &os, const pair< T1, T2 >& p) {
  os << p.first << " " << p.second;
  return os;
}

template< typename T1, typename T2 >
istream &operator>>(istream &is, pair< T1, T2 > &p) {
  is >> p.first >> p.second;
  return is;
}

template< typename T >
ostream &operator<<(ostream &os, const vector< T > &v) {
  for(int i = 0; i < (int) v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template< typename T >
istream &operator>>(istream &is, vector< T > &v) {
  for(T &in : v) is >> in;
  return is;
}

template< typename T1, typename T2 >
inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }

template< typename T1, typename T2 >
inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); }

template< typename T = int64 >
vector< T > make_v(size_t a) {
  return vector< T >(a);
}

template< typename T, typename... Ts >
auto make_v(size_t a, Ts... ts) {
  return vector< decltype(make_v< T >(ts...)) >(a, make_v< T >(ts...));
}

template< typename T, typename V >
typename enable_if< is_class< T >::value == 0 >::type fill_v(T &t, const V &v) {
  t = v;
}

template< typename T, typename V >
typename enable_if< is_class< T >::value != 0 >::type fill_v(T &t, const V &v) {
  for(auto &e : t) fill_v(e, v);
}

template< typename F >
struct FixPoint : F {
  explicit FixPoint(F &&f) : F(forward< F >(f)) {}

  template< typename... Args >
  decltype(auto) operator()(Args &&... args) const {
    return F::operator()(*this, forward< Args >(args)...);
  }
};
 
template< typename F >
inline decltype(auto) MFP(F &&f) {
  return FixPoint< F >{forward< F >(f)};
}
#line 4 "test/verify/aoj-dpl-5-i.test.cpp"

#line 2 "math/combinatorics/montgomery-mod-int.hpp"

template< uint32_t mod_, bool fast = false >
struct MontgomeryModInt {
private:
  using mint = MontgomeryModInt;
  using i32 = int32_t;
  using i64 = int64_t;
  using u32 = uint32_t;
  using u64 = 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 ostream &operator<<(ostream &os, const mint &p) {
    return os << p.val();
  }

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

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

template< uint32_t mod >
using modint = MontgomeryModInt< mod >;
using modint998244353 = modint< 998244353 >;
using modint1000000007 = modint< 1000000007 >;
#line 6 "test/verify/aoj-dpl-5-i.test.cpp"

#line 1 "math/combinatorics/enumeration.hpp"
/**
 * @brief Enumeration(組み合わせ)
 */
template< typename T >
struct Enumeration {
private:
  static vector< T > _fact, _finv, _inv;

  inline static void expand(size_t sz) {
    if(_fact.size() < sz + 1) {
      int pre_sz = 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(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 >
vector< T > Enumeration< T >::_fact = vector< T >();
template< typename T >
vector< T > Enumeration< T >::_finv = vector< T >();
template< typename T >
vector< T > Enumeration< T >::_inv = vector< T >();
#line 2 "math/combinatorics/stirling-number-second.hpp"

/**
 * @brief Stirling Number Second(第2種スターリング数)
 * 
 */
template< typename T >
T stirling_number_second(int n, int k) {
  Enumeration< T > table(k);
  T ret = 0;
  for(int i = 0; i <= k; i++) {
    auto add = T(i).pow(n) * table.C(k, i);
    if((k - i) & 1) ret -= add;
    else ret += add;
  }
  return ret * table.finv(k);
}
#line 8 "test/verify/aoj-dpl-5-i.test.cpp"

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

Test cases

Env	Name	Status	Elapsed	Memory
g++	00_sample_01.in	AC	6 ms	4 MB
g++	00_sample_02.in	AC	6 ms	4 MB
g++	00_sample_03.in	AC	6 ms	4 MB
g++	01_corner_00.in	AC	6 ms	4 MB
g++	01_corner_01.in	AC	6 ms	4 MB
g++	01_corner_02.in	AC	6 ms	4 MB
g++	02_maximum_00.in	AC	6 ms	4 MB
g++	02_maximum_01.in	AC	7 ms	4 MB
g++	03_random_00.in	AC	6 ms	4 MB
g++	03_random_01.in	AC	6 ms	3 MB
g++	03_random_02.in	AC	6 ms	4 MB
g++	03_random_03.in	AC	6 ms	4 MB
g++	03_random_04.in	AC	6 ms	4 MB
g++	03_random_05.in	AC	6 ms	4 MB
g++	03_random_06.in	AC	6 ms	4 MB
g++	03_random_07.in	AC	6 ms	4 MB
g++	03_random_08.in	AC	6 ms	4 MB
g++	03_random_09.in	AC	6 ms	4 MB
g++	03_random_10.in	AC	6 ms	4 MB
g++	03_random_11.in	AC	6 ms	4 MB
g++	03_random_12.in	AC	6 ms	4 MB
g++	03_random_13.in	AC	6 ms	4 MB
g++	03_random_14.in	AC	6 ms	4 MB
g++	03_random_15.in	AC	6 ms	4 MB
g++	03_random_16.in	AC	6 ms	4 MB
g++	03_random_17.in	AC	6 ms	4 MB
g++	03_random_18.in	AC	6 ms	4 MB
g++	03_random_19.in	AC	6 ms	4 MB
g++	04_corner_01.in	AC	6 ms	4 MB
g++	04_corner_02.in	AC	6 ms	4 MB
clang++	00_sample_01.in	AC	6 ms	4 MB
clang++	00_sample_02.in	AC	6 ms	4 MB
clang++	00_sample_03.in	AC	6 ms	4 MB
clang++	01_corner_00.in	AC	6 ms	4 MB
clang++	01_corner_01.in	AC	6 ms	4 MB
clang++	01_corner_02.in	AC	6 ms	4 MB
clang++	02_maximum_00.in	AC	6 ms	4 MB
clang++	02_maximum_01.in	AC	6 ms	4 MB
clang++	03_random_00.in	AC	6 ms	4 MB
clang++	03_random_01.in	AC	6 ms	4 MB
clang++	03_random_02.in	AC	6 ms	4 MB
clang++	03_random_03.in	AC	6 ms	4 MB
clang++	03_random_04.in	AC	6 ms	4 MB
clang++	03_random_05.in	AC	6 ms	4 MB
clang++	03_random_06.in	AC	6 ms	4 MB
clang++	03_random_07.in	AC	6 ms	4 MB
clang++	03_random_08.in	AC	6 ms	4 MB
clang++	03_random_09.in	AC	6 ms	4 MB
clang++	03_random_10.in	AC	6 ms	4 MB
clang++	03_random_11.in	AC	6 ms	4 MB
clang++	03_random_12.in	AC	6 ms	4 MB
clang++	03_random_13.in	AC	6 ms	4 MB
clang++	03_random_14.in	AC	6 ms	4 MB
clang++	03_random_15.in	AC	6 ms	4 MB
clang++	03_random_16.in	AC	6 ms	4 MB
clang++	03_random_17.in	AC	6 ms	4 MB
clang++	03_random_18.in	AC	6 ms	4 MB
clang++	03_random_19.in	AC	6 ms	4 MB
clang++	04_corner_01.in	AC	6 ms	4 MB
clang++	04_corner_02.in	AC	6 ms	4 MB

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