結果

問題 No.1275 綺麗な式
コンテスト
ユーザー Imperi_Night
提出日時 2020-10-30 21:46:23
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 2 ms / 2,000 ms
コード長 7,161 bytes
コンパイル時間 1,060 ms
コンパイル使用メモリ 131,120 KB
最終ジャッジ日時 2025-01-15 17:04:47
ジャッジサーバーID
（参考情報） 		judge3 / judge4
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ファイルパターン 結果
sample AC * 2
other AC * 60
権限があれば一括ダウンロードができます

ソースコード

diff # 

#line 1 "main.cpp"
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <chrono>
#include <cmath>
#include <complex>
#include <cstdint>
#include <cstdlib>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <type_traits>
#include <unordered_map>
#include <utility>
#include <vector>

/* template start */

using i64 = std::int_fast64_t;
using u64 = std::uint_fast64_t;

#define rep(i, a, b) for (i64 i = (a); (i) < (b); (i)++)
#define all(i) i.begin(), i.end()

#ifdef LOCAL
#define debug(...)                                                    \
  std::cerr << "LINE: " << __LINE__ << "  [" << #__VA_ARGS__ << "]:", \
      debug_out(__VA_ARGS__)
#else
#define debug(...)
#endif

void debug_out() { std::cerr << std::endl; }

template <typename Head, typename... Tail>
void debug_out(Head h, Tail... t) {
  std::cerr << " " << h;
  if (sizeof...(t) > 0) std::cout << " :";
  debug_out(t...);
}

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

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

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 Num>
constexpr Num mypow(Num a, u64 b, Num id = 1) {
  if (b == 0) return id;
  Num x = id;
  while (b > 0) {
    if (b & 1) x *= a;
    a *= a;
    b >>= 1;
  }
  return x;
}

template <typename T>
std::vector<std::pair<std::size_t, T>> enumerate(const std::vector<T>& data) {
  std::vector<std::pair<std::size_t, T>> ret;
  for (std::size_t index = 0; index < data.size(); index++)
    ret.emplace_back(index, data[index]);
  return ret;
}

/* template end */

#line 2 "/home/imperi/cp-library/lib/utility/modint.hpp"

/*
  author:noshi91
  reference:https://noshi91.hatenablog.com/entry/2019/03/31/174006
            https://github.com/noshi91/Library/blob/master/other/modint.cpp

  1つめのmodintにoperator==,!=を追加したものです

  thx @noshi91!!
*/

#line 14 "/home/imperi/cp-library/lib/utility/modint.hpp"

template <std::uint_fast64_t Modulus>
class modint {
  using u64 = std::uint_fast64_t;

 public:
  u64 a;

  constexpr modint(const u64 x = 0) noexcept : a(x % Modulus) {}
  constexpr u64 &value() noexcept { return a; }
  constexpr const u64 &value() const noexcept { return a; }
  constexpr bool operator==(const modint rhs) const noexcept {
    return a == rhs.a;
  }
  constexpr bool operator!=(const modint rhs) const noexcept {
    return !(*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) 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 = Modulus - 2;
    while (exp) {
      if (exp % 2) {
        *this *= rhs;
      }
      rhs *= rhs;
      exp /= 2;
    }
    return *this;
  }
};
#line 100 "main.cpp"

constexpr u64 MOD=1000000007;
using mint=modint<MOD>;

#line 2 "/home/imperi/cp-library/lib/math/Matrix.hpp"

#line 6 "/home/imperi/cp-library/lib/math/Matrix.hpp"

template <typename Field, std::size_t ROW, std::size_t COLUMN>
class Matrix {
 public:
  using value_t = Field;
  using size_t = std::size_t;
  static constexpr size_t row = ROW;
  static constexpr size_t column = COLUMN;

  std::array<std::array<value_t, COLUMN>, ROW> a;

  explicit Matrix(const value_t init = value_t()) {
    std::fill(a[0].begin(), a[ROW - 1].end(), init);
  }

  Matrix(const std::array<std::array<Field, COLUMN>, ROW>& a_) : a(a_) {}

  constexpr value_t& operator()(size_t i, size_t j) { return a[i][j]; }
  constexpr bool operator==(const Matrix& rhs) {
    for (size_t i = 0; i < ROW; i++) {
      for (size_t j = 0; j < COLUMN; j++) {
        if (a[i][j] != rhs.a[i][j]) return false;
      }
    }
    return true;
  }
  constexpr bool operator!=(const Matrix& rhs) { return !(*this == rhs); }

  constexpr Matrix operator+(const Matrix rhs) { return Matrix(*this) += rhs; }
  constexpr Matrix operator-(const Matrix rhs) { return Matrix(*this) -= rhs; }

  template <size_t NEWCOLUMN>
  constexpr Matrix<Field, ROW, NEWCOLUMN> operator*(
      const Matrix<Field, COLUMN, NEWCOLUMN> rhs) {
    Matrix<Field, ROW, NEWCOLUMN> tmp;
    for (size_t r = 0; r < ROW; r++) {
      for (size_t c = 0; c < NEWCOLUMN; c++) {
        for (size_t i = 0; i < COLUMN; i++) {
          tmp.a[r][c] += a[r][i] * rhs.a[i][c];
        }
      }
    }
    return tmp;
  }

  constexpr Matrix& operator+=(const Matrix& rhs) {
    for (size_t i = 0; i < ROW; i++) {
      for (size_t j = 0; j < COLUMN; j++) {
        a[i][j] += rhs.a[i][j];
      }
    }
    return *this;
  }
  constexpr Matrix& operator-=(const Matrix& rhs) {
    for (size_t i = 0; i < ROW; i++) {
      for (size_t j = 0; j < COLUMN; j++) {
        a[i][j] -= rhs.a[i][j];
      }
    }
  }
  constexpr Matrix& operator*=(const Matrix<Field, COLUMN, COLUMN>& rhs) {
    std::array<std::array<value_t, COLUMN>, ROW> tmp;
    std::fill(tmp[0].begin(), tmp[ROW - 1].end(), 0);
    for (size_t r = 0; r < ROW; r++) {
      for (size_t c = 0; c < COLUMN; c++) {
        for (size_t i = 0; i < COLUMN; i++) {
          tmp[r][c] += a[r][i] * rhs.a[i][c];
        }
      }
    }
    a = std::move(tmp);
    return *this;
  }

  constexpr static Matrix id() {
    static_assert(ROW == COLUMN, "ROW must be equal to COLUMN");
    Matrix<Field, ROW, COLUMN> tmp;
    for (size_t i = 0; i < ROW; i++) tmp.a[i][i] = 1;
    return tmp;
  }

  void print(){
    for(size_t r=0;r<ROW;r++){
      for(size_t c=0;c<COLUMN;c++){
        std::cout<<a[r][c]<<" ";
      }
      std::cout<<"\n";
    }
  }
};
#line 105 "main.cpp"

using mat = Matrix<mint,2,2>;

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

  i64 a,b,n;
  std::cin>>a>>b>>n;

  mat ret = mat::id();

  mat x({{ {a,b},{1,a}}});

  u64 bit = n;

  while(bit>0){
    if(bit&1)ret *= x;
    x*=x;
    bit>>=1;
  }

  std::cout<<(ret(0,0)*2).value()<<"\n";

  return 0;
}
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