#1111664 (C++23) No.3226 2×2行列累乗

• 問題: No.3226 2×2行列累乗
• ユーザー: a01sa01to
• 提出日時: 2025-08-11 08:40:25
• 言語: C++23 (gcc 13.3.0 + boost 1.87.0)
• 結果: WA
• 実行時間: -
• コード長: 13,415 bytes
• コンパイル時間: 3,214 ms
• コンパイル使用メモリ: 281,468 KB
• 実行使用メモリ: 7,720 KB
• 最終ジャッジ日時: 2025-08-11 08:40:30
• 合計ジャッジ時間: 4,089 ms
• ジャッジサーバーID （参考情報）: judge4 / judge5

ファイルパターン	結果
sample	AC * 3
other	AC * 12 WA * 15

ソースコード

#line 1 "main.cpp"
#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (n); ++i)
using ll = long long;
using ull = unsigned long long;
#line 2 "my-library\\library\\data-structure\\matrix.hpp"
#line 4 "my-library\\library\\data-structure\\matrix.hpp"
#include <concepts>
#line 7 "my-library\\library\\data-structure\\matrix.hpp"
using namespace std;
#line 2 "my-library\\library\\_internal\\types.hpp"
#line 4 "my-library\\library\\_internal\\types.hpp"
using namespace std;
#line 2 "my-library\\library\\_internal\\modint-base.hpp"
#line 4 "my-library\\library\\_internal\\modint-base.hpp"
#include <type_traits>
using namespace std;
namespace asalib {
  namespace _internal {
    class modint_base {};
    template<typename T>
    concept is_modint = is_base_of_v<modint_base, T>;
  }
}
#line 7 "my-library\\library\\_internal\\types.hpp"
namespace asalib {
  namespace _internal {
    template<class T>
    concept integral_like = integral<T> || is_modint<T>;
    template<class T>
    concept floating_like = floating_point<T>;
    template<class T>
    concept numeric_like = integral_like<T> || floating_like<T>;
    template<class T>
    T plus(T a, T b) { return a + b; }
    template<class T>
    T minus(T a, T b) { return a - b; }
    template<class T>
    T zero() { return 0; }
  }
}
#line 10 "my-library\\library\\data-structure\\matrix.hpp"
namespace asalib {
  namespace matrix {
    template<_internal::numeric_like T>
    class Matrix {
      public:
      constexpr Matrix(): _n_row(0), _n_col(0) {};
      constexpr Matrix(size_t n_row, size_t n_col): _n_row(n_row), _n_col(n_col) {
        _data.resize(n_row, valarray<T>(n_col));
      };
      constexpr Matrix(size_t n_row, size_t n_col, T x): _n_row(n_row), _n_col(n_col) {
        _data.resize(n_row, valarray<T>(n_col, x));
      };
      inline constexpr T& at(size_t i, size_t j) {
        assert(i < _n_row);
        assert(j < _n_col);
        return _data[i][j];
      }
      inline constexpr T at(size_t i, size_t j) const {
        assert(i < _n_row);
        assert(j < _n_col);
        return _data[i][j];
      }
      inline constexpr Matrix& operator+=(const T& x) {
        _data += x;
        return *this;
      }
      inline constexpr Matrix& operator-=(const T& x) {
        _data -= x;
        return *this;
      }
      inline constexpr Matrix& operator*=(const T& x) {
        _data *= x;
        return *this;
      }
      inline constexpr Matrix& operator/=(const T& x) {
        _data /= x;
        return *this;
      }
      inline constexpr Matrix& operator%=(const T& x) {
        _data %= x;
        return *this;
      }
      inline constexpr Matrix operator+(const T& x) const { return Matrix(*this) += x; }
      inline constexpr Matrix operator-(const T& x) const { return Matrix(*this) -= x; }
      inline constexpr Matrix operator*(const T& x) const { return Matrix(*this) *= x; }
      inline constexpr Matrix operator/(const T& x) const { return Matrix(*this) /= x; }
      inline constexpr Matrix operator%(const T& x) const { return Matrix(*this) %= x; }
      inline constexpr Matrix& operator+=(const Matrix& x) {
        assert(_n_row == x._n_row);
        assert(_n_col == x._n_col);
        _data += x._data;
        return *this;
      }
      inline constexpr Matrix& operator-=(const Matrix& x) {
        assert(_n_row == x._n_row);
        assert(_n_col == x._n_col);
        _data -= x._data;
        return *this;
      }
      inline constexpr Matrix& operator*=(const Matrix& x) {
        assert(_n_col == x._n_row);
        Matrix res(_n_row, x._n_col);
        for (size_t i = 0; i < _n_row; ++i) {
          for (size_t k = 0; k < _n_col; ++k) {
            for (size_t j = 0; j < x._n_col; ++j) {
              res._data[i][j] += _data[i][k] * x._data[k][j];
            }
          }
        }
        return *this = res;
      }
      inline constexpr Matrix operator+(const Matrix& x) const { return Matrix(*this) += x; }
      inline constexpr Matrix operator-(const Matrix& x) const { return Matrix(*this) -= x; }
      inline constexpr Matrix operator*(const Matrix& x) const { return Matrix(*this) *= x; }
      inline constexpr bool operator==(const Matrix& x) const { return _n_row == x._n_row && _n_col == x._n_col && _data == x._data; }
      inline constexpr bool operator!=(const Matrix& x) const { return !(*this == x); }
      inline constexpr bool operator<(const Matrix& x) const { return _data < x._data; }
      inline constexpr Matrix transpose() const {
        Matrix res(_n_col, _n_row);
        for (size_t i = 0; i < _n_row; ++i) {
          for (size_t j = 0; j < _n_col; ++j) {
            res._data[j][i] = _data[i][j];
          }
        }
        return res;
      }
      template<integral U>
      inline constexpr Matrix pow(U x) const {
        assert(_n_row == _n_col);
        Matrix res = I(_n_row);
        Matrix a(*this);
        while (x) {
          if (x & 1) res *= a;
          a *= a;
          x >>= 1;
        }
        return res;
      }
      inline static constexpr Matrix I(size_t n) {
        Matrix res(n, n);
        for (size_t i = 0; i < n; ++i) {
          res._data[i][i] = 1;
        }
        return res;
      }
      inline constexpr size_t n_row() const { return _n_row; }
      inline constexpr size_t n_col() const { return _n_col; }
      private:
      size_t _n_row, _n_col;
      valarray<valarray<T>> _data;
      public:
      inline constexpr T determinant() const;
      template<_internal::numeric_like U>
      inline constexpr U determinant() const;
    };
  }
}
#line 2 "my-library\\library\\data-structure\\modint.hpp"
#line 8 "my-library\\library\\data-structure\\modint.hpp"
using namespace std;
#line 2 "my-library\\library\\math\\extgcd.hpp"
#line 4 "my-library\\library\\math\\extgcd.hpp"
#include <optional>
#line 6 "my-library\\library\\math\\extgcd.hpp"
using namespace std;
namespace asalib {
  namespace math {
    template<integral T>
    constexpr optional<pair<T, T>> extgcd(T a, T b, T c) {
      if (b == 0) {
        if (c % a != 0) return nullopt;
        return make_pair(c / a, 0);
      }
      auto res = extgcd(b, a % b, c);
      if (!res) return nullopt;
      auto [x, y] = *res;
      return make_pair(y, x - (a / b) * y);
    }
  }
}
#line 12 "my-library\\library\\data-structure\\modint.hpp"
namespace asalib {
  namespace ds {
    template<unsigned int mod>
      requires(mod >= 1)
    class static_modint: private _internal::modint_base {
      using mint = static_modint;
      using uint = unsigned int;
      using ll = long long;
      using ull = unsigned long long;
      public:
      inline constexpr static_modint(): _val(0) {};
      template<integral T>
      inline constexpr static_modint(const T& x) {
        if constexpr (is_signed_v<T>) {
          ll y = x % (ll) mod;
          if (y < 0) y += mod;
          _val = y;
        }
        else {
          _val = x % mod;
        }
      }
      friend inline constexpr mint operator+(const mint& l, const mint& r) { return mint(l) += r; }
      friend inline constexpr mint operator-(const mint& l, const mint& r) { return mint(l) -= r; }
      friend inline constexpr mint operator*(const mint& l, const mint& r) { return mint(l) *= r; }
      friend inline constexpr mint operator/(const mint& l, const mint& r) { return mint(l) /= r; }
      inline constexpr mint operator+() const { return *this; }
      inline constexpr mint operator-() const { return 0 - *this; }
      inline constexpr mint& operator+=(const mint& other) {
        _val += other._val;
        if (_val >= mod) _val -= mod;
        return *this;
      }
      inline constexpr mint& operator-=(const mint& other) {
        _val -= other._val;
        if (_val >= mod) _val += mod;
        return *this;
      }
      inline constexpr mint& operator*=(const mint& other) {
        ull z = _val;
        z *= other._val;
        _val = z % mod;
        return *this;
      }
      inline constexpr mint& operator/=(const mint& other) { return *this = *this * other.inv(); }
      inline constexpr mint& operator++() {
        _val++;
        if (_val == mod) _val = 0;
        return *this;
      }
      inline constexpr mint& operator--() {
        if (_val == 0) _val = mod;
        _val--;
        return *this;
      }
      inline constexpr mint operator++(int) {
        mint res = *this;
        ++*this;
        return res;
      }
      inline constexpr mint operator--(int) {
        mint res = *this;
        --*this;
        return res;
      }
      inline constexpr bool operator==(const mint& r) const { return _val == r._val; }
      inline constexpr bool operator!=(const mint& r) const { return _val != r._val; }
      inline constexpr bool operator<(const mint& r) const { return _val < r._val; }
      template<integral T>
      inline constexpr mint pow(T x) const {
        assert(x >= 0);
        mint res = 1, base = *this;
        while (x) {
          if (x & 1) res *= base;
          base *= base;
          x >>= 1;
        }
        return res;
      }
      inline constexpr mint inv() const {
        if constexpr (is_prime_mod) return pow(mod - 2);
        else {
          if (gcd(_val, mod) != 1) throw invalid_argument("Modular inverse does not exist");
          return mint(math::extgcd<long long>(_val, mod, 1).value().first);
        }
      }
      constexpr inline unsigned int val() const { return _val; }
      private:
      uint _val;
      static inline constexpr bool is_prime_mod = []() {
        for (unsigned int i = 2; i * i <= mod; ++i) {
          if (mod % i == 0) return false;
        }
        return true;
      }();
    };
    template<unsigned int id>
    class dynamic_modint: private _internal::modint_base {
      using mint = dynamic_modint;
      using uint = unsigned int;
      using ll = long long;
      using ull = unsigned long long;
      public:
      inline constexpr dynamic_modint(): _val(0) {}
      template<integral T>
      inline constexpr dynamic_modint(const T& x) {
        assert(_mod >= 1);
        if constexpr (is_signed_v<T>) {
          ll y = x % (ll) _mod;
          if (y < 0) y += _mod;
          _val = y;
        }
        else {
          _val = x % _mod;
        }
      };
      friend inline constexpr mint operator+(const mint& l, const mint& r) { return mint(l) += r; }
      friend inline constexpr mint operator-(const mint& l, const mint& r) { return mint(l) -= r; }
      friend inline constexpr mint operator*(const mint& l, const mint& r) { return mint(l) *= r; }
      friend inline constexpr mint operator/(const mint& l, const mint& r) { return mint(l) /= r; }
      inline constexpr mint operator+() const { return *this; }
      inline constexpr mint operator-() const { return 0 - *this; }
      inline constexpr mint& operator+=(const mint& other) {
        _val += other._val;
        if (_val >= _mod) _val -= _mod;
        return *this;
      }
      inline constexpr mint& operator-=(const mint& other) {
        _val -= other._val;
        if (_val >= _mod) _val += _mod;
        return *this;
      }
      inline constexpr mint& operator*=(const mint& other) {
        ull z = _val;
        z *= other._val;
        _val = z % _mod;
        return *this;
      }
      inline constexpr mint& operator/=(const mint& other) { return *this = *this * other.inv(); }
      inline constexpr mint& operator++() {
        _val++;
        if (_val == _mod) _val = 0;
        return *this;
      }
      inline constexpr mint& operator--() {
        if (_val == 0) _val = _mod;
        _val--;
        return *this;
      }
      inline constexpr mint operator++(int) {
        mint res = *this;
        ++*this;
        return res;
      }
      inline constexpr mint operator--(int) {
        mint res = *this;
        --*this;
        return res;
      }
      inline constexpr bool operator==(const mint& r) const { return _val == r._val; }
      inline constexpr bool operator!=(const mint& r) const { return _val != r._val; }
      inline constexpr bool operator<(const mint& r) const { return _val < r._val; }
      template<integral T>
      inline constexpr mint pow(T x) const {
        assert(x >= 0);
        mint res = 1, base = *this;
        while (x) {
          if (x & 1) res *= base;
          base *= base;
          x >>= 1;
        }
        return res;
      }
      inline constexpr mint inv() const {
        if (gcd(_val, _mod) != 1) throw invalid_argument("Modular inverse does not exist");
        return mint(math::extgcd<long long>(_val, _mod, 1).value().first);
      }
      inline constexpr uint val() const { return _val; }
      inline constexpr static uint mod() { return _mod; }
      inline constexpr static void set_mod(uint mod) {
        assert(mod >= 1);
        _mod = mod;
      }
      private:
      uint _val;
      static inline uint _mod;
    };
  }
}
#line 9 "main.cpp"
using mint = asalib::ds::dynamic_modint<0>;
int main() {
  cin.tie(nullptr)->sync_with_stdio(false);
  int a, b, c, d, s, t, n, k;
  cin >> a >> b >> c >> d >> s >> t >> n >> k;
  mint::set_mod(k);
  asalib::matrix::Matrix<mint> M(2, 2), st(2, 1);
  M.at(0, 0) = a, M.at(0, 1) = b, M.at(1, 0) = c, M.at(1, 1) = d;
  st.at(0, 0) = s, st.at(1, 0) = t;
  auto res = M.pow(n) * st;
  cout << res.at(0, 0).val() << ' ' << res.at(1, 0).val() << '\n';
  return 0;
}