Submission #14099426

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Source Code Expand

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

template <class T, class U>
inline bool chmin(T &lhs, const U &rhs) {
  if (lhs > rhs) { lhs = rhs; return true; }
  return false;
}

template <class T, class U>
inline bool chmax(T &lhs, const U &rhs) {
  if (lhs < rhs) { lhs = rhs; return true; }
  return false;
}

struct range {
  using itr = int64_t;
  struct iterator {
    itr i;
    constexpr iterator(itr i_): i(i_) { }
    constexpr void operator ++ () { ++i; }
    constexpr itr operator * () const { return i; }
    constexpr bool operator != (iterator x) const { return i != x.i; }
  };
  const iterator l, r;
  constexpr range(itr l_, itr r_): l(l_), r(std::max(l_, r_)) { }
  constexpr iterator begin() const { return l; }
  constexpr iterator end() const { return r; }
};

struct revrange {
  using itr = int64_t;
  struct iterator {
    itr i;
    constexpr iterator(itr i_): i(i_) { }
    constexpr void operator ++ () { --i; }
    constexpr itr operator * () const { return i; }
    constexpr bool operator != (iterator x) const { return i != x.i; }
  };
  const iterator l, r;
  constexpr revrange(itr l_, itr r_): l(l_ - 1), r(std::max(l_, r_) - 1) { }
  constexpr iterator begin() const { return r; }
  constexpr iterator end() const { return l; }
};

template <uint32_t Modulus>
class modular {
public:
  using value_type = uint32_t;
  using max_type = uint64_t;

  static constexpr value_type mod = Modulus;
  static constexpr value_type get_mod() { return mod; }
  static_assert(mod >= 2, "invalid mod :: smaller than 2");
  static_assert(mod < (value_type(1) << 31), "invalid mod :: over 2^31");

  template <class T>
  static constexpr value_type normalize(T value_) {
    if (value_ < 0) {
      value_ = -value_;
      value_ %= mod;
      if (value_ == 0) return 0;
      return mod - value_;
    }
    return value_ % mod;
  }

private:
  value_type value;

public:
  constexpr modular(): value(0) { }
  template <class T>
  explicit constexpr modular(T value_): value(normalize(value_)) { }
  template <class T>
  explicit constexpr operator T() { return static_cast<T>(value); }

  constexpr value_type get() const { return value; }
  constexpr modular operator - () const { return modular(mod - value); }
  constexpr modular operator ~ () const { return inverse(); }

  constexpr value_type &extract() { return value; }
  constexpr modular inverse() const { return power(mod - 2); }
  constexpr modular power(max_type exp) const {
    modular res(1), mult(*this);
    while (exp > 0) {
      if (exp & 1) res *= mult;
      mult *= mult;
      exp >>= 1;
    }
    return res;
  }

  constexpr modular operator + (const modular &rhs) const { return modular(*this) += rhs; }
  constexpr modular& operator += (const modular &rhs) { 
    if ((value += rhs.value) >= mod) value -= mod; 
    return *this; 
  }

  constexpr modular operator - (const modular &rhs) const { return modular(*this) -= rhs; }
  constexpr modular& operator -= (const modular &rhs) { 
    if ((value += mod - rhs.value) >= mod) value -= mod; 
    return *this; 
  }

  constexpr modular operator * (const modular &rhs) const { return modular(*this) *= rhs; }
  constexpr modular& operator *= (const modular &rhs) { 
    value = (max_type) value * rhs.value % mod;
    return *this;
  }

  constexpr modular operator / (const modular &rhs) const { return modular(*this) /= rhs; }
  constexpr modular& operator /= (const modular &rhs) { return (*this) *= rhs.inverse(); }

  constexpr bool zero() const { return value == 0; }
  constexpr bool operator == (const modular &rhs) const { return value == rhs.value; }
  constexpr bool operator != (const modular &rhs) const { return value != rhs.value; }
  friend std::ostream& operator << (std::ostream &stream, const modular &rhs) {
    return stream << rhs.value;
  }

};

using m32 = modular<1000000007>;

using i32 = int32_t;
using i64 = int64_t;
using u32 = uint32_t;
using u64 = uint64_t;

constexpr i32 inf32 = (i32(1) << 30) - 1;
constexpr i64 inf64 = (i64(1) << 62) - 1;

int main() {
  i32 N, A, B;
  std::cin >> N >> A >> B;
  N += 2;
  if (A > B) {
    std::swap(A, B);
  }
  std::vector<std::array<m32, 2>> dp1(N + 1);
  for (auto i: range(0, N + 1)) {
    for (auto j: range(0, 2)) {
      dp1[i][j] = (m32) 0;
    }
  }
  dp1[0][1] = (m32) 1;
  for (auto i: range(0, N + 1)) {
    { // extend 0 (greater than or equal to A)
      for (auto j: range(A, N + 1)) {
        if (i + j <= N) {
          dp1[i + j][1] += dp1[i][0];
        }
      }
    }
    { // extend 1 (any length)
      for (auto j: range(1, N + 1)) {
        if (i + j <= N) {
          dp1[i + j][0] += dp1[i][1];
        }
      }
    }
  }
  std::vector<std::array<std::array<m32, 2>, 2>> dp2(N + 1);
  for (auto i: range(0, N + 1)) {
    for (auto j: range(0, 2)) {
      for (auto k: range(0, 2)) {
        dp2[i][j][k] = (m32) 0;
      }
    }
  }
  dp2[0][1][0] = (m32) 1;
  for (auto i: range(0, N + 1)) {
    for (auto k: range(0, 2)) {
      { // extend 0 (less than A)
        for (auto j: range(1, A)) {
          if (i + j <= N) {
            dp2[i + j][1][k] += dp2[i][0][k];
          }
        }
      }
      { // extend 1 (any length)
        for (auto j: range(1, N + 1)) {
          if (i + j <= N) {
            auto len = j;
            if (i == 0) --len;
            if (i + j == N) --len;
            if (len >= B) {
              dp2[i + j][0][1] += dp2[i][1][k] * dp1[j][0];
            }
            else {
              dp2[i + j][0][k] += dp2[i][1][k] * dp1[j][0];
            }
          }
        }
      }
    }
  }
  std::cout << dp2[N][0][1] << '\n';
  return 0;
}

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