test/yukicoder/665/main.test.cpp

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• Last update: 2021-04-23 23:44:44+09:00
• Problem: https://yukicoder.me/problems/no/665
• Link: View error logs on GitHub Actions

Depends on

• Bernoulli number (Mylib/Combinatorics/bernoulli_number.cpp)
• Factorial table (Mylib/Combinatorics/factorial_table.cpp)
• Modint (Mylib/Number/Mint/mint.cpp)

Code

#define PROBLEM "https://yukicoder.me/problems/no/665"

#include <iostream>
#include "Mylib/Combinatorics/bernoulli_number.cpp"
#include "Mylib/Combinatorics/factorial_table.cpp"
#include "Mylib/Number/Mint/mint.cpp"

namespace hl = haar_lib;

using mint           = hl::modint<1000000007>;
const static auto ft = hl::factorial_table<mint>(30000);

int main() {
  std::cin.tie(0);
  std::ios::sync_with_stdio(false);

  int64_t n, k;
  std::cin >> n >> k;

  auto b = hl::bernoulli_number<ft>(k);

  mint ans = 0;

  for (int64_t i = 0; i <= k; ++i) {
    ans += ft.C(k + 1, i) * b[i] * mint::pow(n + 1, k + 1 - i);
  }

  ans /= k + 1;

  std::cout << ans << std::endl;

  return 0;
}

#line 1 "test/yukicoder/665/main.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/665"

#include <iostream>
#line 2 "Mylib/Combinatorics/bernoulli_number.cpp"
#include <cstdint>
#include <vector>
#line 2 "Mylib/Combinatorics/factorial_table.cpp"
#include <cassert>
#line 5 "Mylib/Combinatorics/factorial_table.cpp"

namespace haar_lib {
  template <typename T>
  class factorial_table {
  public:
    using value_type = T;

  private:
    int N_;
    std::vector<T> f_table_, if_table_;

  public:
    factorial_table() {}
    factorial_table(int N) : N_(N) {
      f_table_.assign(N + 1, 1);
      if_table_.assign(N + 1, 1);

      for (int i = 1; i <= N; ++i) {
        f_table_[i] = f_table_[i - 1] * i;
      }

      if_table_[N] = f_table_[N].inv();

      for (int i = N; --i >= 0;) {
        if_table_[i] = if_table_[i + 1] * (i + 1);
      }
    }

    T factorial(int64_t i) const {
      assert(0 <= i and i <= N_);
      return f_table_[i];
    }

    T inv_factorial(int64_t i) const {
      assert(0 <= i and i <= N_);
      return if_table_[i];
    }

    T P(int64_t n, int64_t k) const {
      if (n < k or n < 0 or k < 0) return 0;
      return factorial(n) * inv_factorial(n - k);
    }

    T C(int64_t n, int64_t k) const {
      if (n < k or n < 0 or k < 0) return 0;
      return P(n, k) * inv_factorial(k);
    }

    T H(int64_t n, int64_t k) const {
      if (n == 0 and k == 0) return 1;
      return C(n + k - 1, k);
    }
  };
}  // namespace haar_lib
#line 5 "Mylib/Combinatorics/bernoulli_number.cpp"

namespace haar_lib {
  template <
      const auto &ft,
      typename T = typename std::remove_reference_t<decltype(ft)>::value_type>
  std::vector<T> bernoulli_number(int n) {
    std::vector<T> ret(n + 1);

    ret[0] = 1;

    for (int64_t i = 1; i <= n; ++i) {
      for (int k = 0; k <= i - 1; ++k) {
        ret[i] += ft.C(i + 1, k) * ret[k];
      }
      ret[i] /= i + 1;
      ret[i] = -ret[i];
    }

    return ret;
  }
}  // namespace haar_lib
#line 3 "Mylib/Number/Mint/mint.cpp"
#include <utility>

namespace haar_lib {
  template <int32_t M>
  class modint {
    uint32_t val_;

  public:
    constexpr static auto mod() { return M; }

    constexpr modint() : val_(0) {}
    constexpr modint(int64_t n) {
      if (n >= M)
        val_ = n % M;
      else if (n < 0)
        val_ = n % M + M;
      else
        val_ = n;
    }

    constexpr auto &operator=(const modint &a) {
      val_ = a.val_;
      return *this;
    }
    constexpr auto &operator+=(const modint &a) {
      if (val_ + a.val_ >= M)
        val_ = (uint64_t) val_ + a.val_ - M;
      else
        val_ += a.val_;
      return *this;
    }
    constexpr auto &operator-=(const modint &a) {
      if (val_ < a.val_) val_ += M;
      val_ -= a.val_;
      return *this;
    }
    constexpr auto &operator*=(const modint &a) {
      val_ = (uint64_t) val_ * a.val_ % M;
      return *this;
    }
    constexpr auto &operator/=(const modint &a) {
      val_ = (uint64_t) val_ * a.inv().val_ % M;
      return *this;
    }

    constexpr auto operator+(const modint &a) const { return modint(*this) += a; }
    constexpr auto operator-(const modint &a) const { return modint(*this) -= a; }
    constexpr auto operator*(const modint &a) const { return modint(*this) *= a; }
    constexpr auto operator/(const modint &a) const { return modint(*this) /= a; }

    constexpr bool operator==(const modint &a) const { return val_ == a.val_; }
    constexpr bool operator!=(const modint &a) const { return val_ != a.val_; }

    constexpr auto &operator++() {
      *this += 1;
      return *this;
    }
    constexpr auto &operator--() {
      *this -= 1;
      return *this;
    }

    constexpr auto operator++(int) {
      auto t = *this;
      *this += 1;
      return t;
    }
    constexpr auto operator--(int) {
      auto t = *this;
      *this -= 1;
      return t;
    }

    constexpr static modint pow(int64_t n, int64_t p) {
      if (p < 0) return pow(n, -p).inv();

      int64_t ret = 1, e = n % M;
      for (; p; (e *= e) %= M, p >>= 1)
        if (p & 1) (ret *= e) %= M;
      return ret;
    }

    constexpr static modint inv(int64_t a) {
      int64_t b = M, u = 1, v = 0;

      while (b) {
        int64_t t = a / b;
        a -= t * b;
        std::swap(a, b);
        u -= t * v;
        std::swap(u, v);
      }

      u %= M;
      if (u < 0) u += M;

      return u;
    }

    constexpr static auto frac(int64_t a, int64_t b) { return modint(a) / modint(b); }

    constexpr auto pow(int64_t p) const { return pow(val_, p); }
    constexpr auto inv() const { return inv(val_); }

    friend constexpr auto operator-(const modint &a) { return modint(M - a.val_); }

    friend constexpr auto operator+(int64_t a, const modint &b) { return modint(a) + b; }
    friend constexpr auto operator-(int64_t a, const modint &b) { return modint(a) - b; }
    friend constexpr auto operator*(int64_t a, const modint &b) { return modint(a) * b; }
    friend constexpr auto operator/(int64_t a, const modint &b) { return modint(a) / b; }

    friend std::istream &operator>>(std::istream &s, modint &a) {
      s >> a.val_;
      return s;
    }
    friend std::ostream &operator<<(std::ostream &s, const modint &a) {
      s << a.val_;
      return s;
    }

    template <int N>
    static auto div() {
      static auto value = inv(N);
      return value;
    }

    explicit operator int32_t() const noexcept { return val_; }
    explicit operator int64_t() const noexcept { return val_; }
  };
}  // namespace haar_lib
#line 7 "test/yukicoder/665/main.test.cpp"

namespace hl = haar_lib;

using mint           = hl::modint<1000000007>;
const static auto ft = hl::factorial_table<mint>(30000);

int main() {
  std::cin.tie(0);
  std::ios::sync_with_stdio(false);

  int64_t n, k;
  std::cin >> n >> k;

  auto b = hl::bernoulli_number<ft>(k);

  mint ans = 0;

  for (int64_t i = 0; i <= k; ++i) {
    ans += ft.C(k + 1, i) * b[i] * mint::pow(n + 1, k + 1 - i);
  }

  ans /= k + 1;

  std::cout << ans << std::endl;

  return 0;
}

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