#381208 (C++14) No.891 隣接3項間の漸化式

• 問題: No.891 隣接3項間の漸化式
• ユーザー: noshi91
• 提出日時: 2019-09-20 21:30:33
• 言語: C++14 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 2 ms / 2,000 ms
• コード長: 9,124 bytes
• コンパイル時間: 816 ms
• コンパイル使用メモリ: 79,440 KB
• 実行使用メモリ: 5,376 KB
• 最終ジャッジ日時: 2024-09-14 16:26:59
• 合計ジャッジ時間: 2,018 ms
• ジャッジサーバーID （参考情報）: judge5 / judge1

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 5,248 KB
testcase_01	AC	2 ms; 5,376 KB
testcase_02	AC	2 ms; 5,376 KB
testcase_03	AC	2 ms; 5,376 KB
testcase_04	AC	2 ms; 5,376 KB
testcase_05	AC	2 ms; 5,376 KB
testcase_06	AC	2 ms; 5,376 KB
testcase_07	AC	2 ms; 5,376 KB
testcase_08	AC	2 ms; 5,376 KB
testcase_09	AC	2 ms; 5,376 KB
testcase_10	AC	2 ms; 5,376 KB
testcase_11	AC	2 ms; 5,376 KB
testcase_12	AC	2 ms; 5,376 KB
testcase_13	AC	2 ms; 5,376 KB
testcase_14	AC	1 ms; 5,376 KB
testcase_15	AC	2 ms; 5,376 KB
testcase_16	AC	2 ms; 5,376 KB
testcase_17	AC	2 ms; 5,376 KB
testcase_18	AC	2 ms; 5,376 KB
testcase_19	AC	2 ms; 5,376 KB
testcase_20	AC	2 ms; 5,376 KB
testcase_21	AC	2 ms; 5,376 KB
testcase_22	AC	2 ms; 5,376 KB
testcase_23	AC	2 ms; 5,376 KB
testcase_24	AC	2 ms; 5,376 KB
testcase_25	AC	2 ms; 5,376 KB
testcase_26	AC	2 ms; 5,376 KB
testcase_27	AC	2 ms; 5,376 KB
testcase_28	AC	2 ms; 5,376 KB
testcase_29	AC	2 ms; 5,376 KB
testcase_30	AC	1 ms; 5,376 KB
testcase_31	AC	2 ms; 5,376 KB
testcase_32	AC	2 ms; 5,376 KB
testcase_33	AC	2 ms; 5,376 KB
testcase_34	AC	2 ms; 5,376 KB
testcase_35	AC	2 ms; 5,376 KB
testcase_36	AC	2 ms; 5,376 KB
testcase_37	AC	2 ms; 5,376 KB
testcase_38	AC	2 ms; 5,376 KB
testcase_39	AC	2 ms; 5,376 KB
testcase_40	AC	2 ms; 5,376 KB
testcase_41	AC	2 ms; 5,376 KB

ソースコード

//#define NDEBUG
#include <cstddef>
#include <cstdint>
#include <iostream>
#include <iterator>
#include <vector>

namespace n91 {

using i8 = std::int_fast8_t;
using i32 = std::int_fast32_t;
using i64 = std::int_fast64_t;
using u8 = std::uint_fast8_t;
using u32 = std::uint_fast32_t;
using u64 = std::uint_fast64_t;
using isize = std::ptrdiff_t;
using usize = std::size_t;

constexpr usize operator"" _z(unsigned long long x) noexcept {
  return static_cast<usize>(x);
}

template <class T> class integral_iterator {
public:
  using difference_type = T;
  using value_type = T;
  using pointer = const value_type *;
  using reference = value_type;
  using iterator_category = std::random_access_iterator_tag;

private:
  using self_type = integral_iterator<value_type>;
  value_type i;

public:
  constexpr integral_iterator() noexcept : i() {}
  explicit constexpr integral_iterator(const value_type i) noexcept : i(i) {}
  constexpr self_type operator++(int) noexcept { return self_type(i++); }
  constexpr self_type operator--(int) noexcept { return self_type(i--); }
  constexpr self_type operator[](const difference_type rhs) const noexcept {
    return self_type(i + rhs);
  }
  constexpr self_type &operator++() noexcept {
    ++i;
    return *this;
  }
  constexpr self_type &operator--() noexcept {
    --i;
    return *this;
  }
  constexpr reference operator*() const noexcept { return i; }
  constexpr self_type operator+(const difference_type rhs) const noexcept {
    return self_type(i + rhs);
  }
  constexpr self_type operator-(const difference_type rhs) const noexcept {
    return self_type(i - rhs);
  }
  constexpr difference_type operator-(const self_type rhs) const noexcept {
    return i - rhs.i;
  }
  constexpr bool operator<(const self_type rhs) const noexcept {
    return i < rhs.i;
  }
  constexpr bool operator<=(const self_type rhs) const noexcept {
    return i <= rhs.i;
  }
  constexpr bool operator>(const self_type rhs) const noexcept {
    return i > rhs.i;
  }
  constexpr bool operator>=(const self_type rhs) const noexcept {
    return i >= rhs.i;
  }
  constexpr bool operator==(const self_type rhs) const noexcept {
    return i == rhs.i;
  }
  constexpr bool operator!=(const self_type rhs) const noexcept {
    return i != rhs.i;
  }
  constexpr self_type &operator+=(const difference_type rhs) noexcept {
    i += rhs;
    return *this;
  }
  constexpr self_type &operator-=(const difference_type rhs) noexcept {
    i -= rhs;
    return *this;
  }
};
template <class T>
constexpr integral_iterator<T> make_int_itr(const T i) noexcept {
  return integral_iterator<T>(i);
}
class rep {
  const usize f, l;

public:
  constexpr rep(const usize f, const usize l) noexcept : f(f), l(l) {}
  constexpr auto begin() const noexcept { return make_int_itr(f); }
  constexpr auto end() const noexcept { return make_int_itr(l); }
};
class revrep {
  const usize f, l;

public:
  revrep(const usize f, const usize l) noexcept : f(l), l(f) {}
  auto begin() const noexcept {
    return std::make_reverse_iterator(make_int_itr(f));
  }
  auto end() const noexcept {
    return std::make_reverse_iterator(make_int_itr(l));
  }
};
template <class T> auto md_vec(const usize n, const T &value) {
  return std::vector<T>(n, value);
}
template <class... Args> auto md_vec(const usize n, Args... args) {
  return std::vector<decltype(md_vec(args...))>(n, md_vec(args...));
}
template <class T> constexpr T difference(const T &a, const T &b) {
  return a < b ? b - a : a - b;
}
template <class T> T scan() {
  T ret;
  std::cin >> ret;
  return ret;
}

} // namespace n91

#include <algorithm>
#include <array>
#include <cassert>
#include <cstddef>
#include <initializer_list>

namespace n91 {

template <class T, std::size_t M, std::size_t N>
class array_matrix : public std::array<std::array<T, N>, M> {
public:
  array_matrix() {
    std::for_each(this->begin(), this->end(), [](auto &row) {
      std::fill(row.begin(), row.end(), static_cast<T>(0));
    });
  }
  array_matrix(std::initializer_list<std::initializer_list<T>> il) {
    assert(il.size() == M);
    auto ar_itr = this->begin();
    const auto ar_end = this->end();
    auto il_itr = il.begin();
    while (ar_itr != ar_end) {
      assert(il_itr->size() == N);
      std::copy(il_itr->begin(), il_itr->end(), ar_itr->begin());
      ++ar_itr;
      ++il_itr;
    }
  }
  array_matrix &operator*=(const array_matrix<T, N, N> &rhs) {
    return *this = *this * rhs;
  }
};

template <class T, std::size_t L, std::size_t M, std::size_t N>
array_matrix<T, L, N> operator*(const array_matrix<T, L, M> &lhs,
                                const array_matrix<T, M, N> &rhs) {
  array_matrix<T, L, N> ret = {};
  for (std::size_t i = static_cast<std::size_t>(0); i != L; ++i) {
    for (std::size_t j = static_cast<std::size_t>(0); j != M; ++j) {
      for (std::size_t k = static_cast<std::size_t>(0); k != N; ++k) {
        ret[i][k] += lhs[i][j] * rhs[j][k];
      }
    }
  }
  return ret;
}

template <class T, std::size_t N> array_matrix<T, N, N> matrix_identity() {
  array_matrix<T, N, N> ret;
  for (std::size_t i = static_cast<std::size_t>(0); i != N; ++i) {
    ret[i][i] = static_cast<T>(1);
  }
  return ret;
}

} // namespace n91

#include <cstdint>

namespace n91 {

constexpr std::uint_fast64_t totient(std::uint_fast64_t x) noexcept {
  using u64 = std::uint_fast64_t;
  u64 ret = x;
  for (u64 i = static_cast<u64>(2); i * i <= x; ++i) {
    if (x % i == static_cast<u64>(0)) {
      ret -= ret / i;
      x /= i;
      while (x % i == static_cast<u64>(0)) {
        x /= i;
      }
    }
  }
  if (x != static_cast<u64>(1)) {
    ret -= ret / x;
  }
  return ret;
}

template <std::uint_fast64_t Modulus,
          std::uint_fast64_t InverseExp =
              totient(Modulus) - static_cast<std::uint_fast64_t>(1)>
class modint {
  using u64 = std::uint_fast64_t;

  static_assert(Modulus < static_cast<u64>(1) << static_cast<u64>(32),
                "Modulus must be less than 2**32");

  u64 a;

  constexpr modint &negate() noexcept {
    if (a != static_cast<u64>(0)) {
      a = Modulus - a;
    }
    return *this;
  }

public:
  constexpr modint(const u64 x = static_cast<u64>(0)) noexcept
      : a(x % Modulus) {}
  constexpr u64 &value() noexcept { return a; }
  constexpr const u64 &value() const noexcept { return a; }
  constexpr modint operator+() const noexcept { return modint(*this); }
  constexpr modint operator-() const noexcept { return modint(*this).negate(); }
  constexpr modint operator+(const modint rhs) const noexcept {
    return modint(*this) += rhs;
  }
  constexpr modint operator-(const modint rhs) const noexcept {
    return modint(*this) -= rhs;
  }
  constexpr modint operator*(const modint rhs) const noexcept {
    return modint(*this) *= rhs;
  }
  constexpr modint operator/(const modint rhs) const noexcept {
    return modint(*this) /= rhs;
  }
  constexpr modint &operator+=(const modint rhs) noexcept {
    a += rhs.a;
    if (a >= Modulus) {
      a -= Modulus;
    }
    return *this;
  }
  constexpr modint &operator-=(const modint rhs) noexcept {
    if (a < rhs.a) {
      a += Modulus;
    }
    a -= rhs.a;
    return *this;
  }
  constexpr modint &operator*=(const modint rhs) noexcept {
    a = a * rhs.a % Modulus;
    return *this;
  }
  constexpr modint &operator/=(modint rhs) noexcept {
    u64 exp = InverseExp;
    while (exp) {
      if (exp % static_cast<u64>(2) != static_cast<u64>(0)) {
        *this *= rhs;
      }
      rhs *= rhs;
      exp /= static_cast<u64>(2);
    }
    return *this;
  }
  constexpr bool operator==(const modint rhs) const noexcept {
    return a == rhs.a;
  }
  constexpr bool operator!=(const modint rhs) const noexcept {
    return a != rhs.a;
  }
};

template <class T, std::uint_fast64_t v> class modint_constant {
public:
  static constexpr T value = static_cast<T>(v);

  using value_type = T;
};

} // namespace n91

#include <functional>
#include <utility>

namespace n91 {

template <class T, class U, class Operate = std::multiplies<T>>
constexpr T power(T base, U exp, const Operate &oper = Operate(),
                  T iden = static_cast<T>(1)) {
  while (exp != static_cast<U>(0)) {
    if (exp % static_cast<U>(2) != static_cast<U>(0)) {
      iden = oper(iden, base);
    }
    exp /= static_cast<U>(2);
    base = oper(base, base);
  }
  return iden;
}

} // namespace n91

#include <algorithm>
#include <iostream>
#include <utility>

namespace n91 {

void main_() {
  using mint = modint<static_cast<u64>(1000000007)>;
  using mat = array_matrix<mint, 2_z, 2_z>;
  const mint a = static_cast<mint>(scan<u64>());
  const mint b = static_cast<mint>(scan<u64>());
  const u64 n = scan<u64>();
  mat step = {{a, static_cast<mint>(1)}, {b, static_cast<mint>(0)}};
  array_matrix<mint, 1_z, 2_z> init = {
      {static_cast<mint>(1), static_cast<mint>(0)}};
  std::cout << (init * power(step, n, std::multiplies<mat>(),
                             matrix_identity<mint, 2_z>()))[0_z][1_z]
                   .value()
            << std::endl;
}

} // namespace n91

int main() {
  n91::main_();
  return 0;
}