#line 1 "main.cpp" #include 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 "library\\data_structure\\matrix.hpp" #line 4 "library\\data_structure\\matrix.hpp" using namespace std; #line 2 "library\\data_structure\\modint.hpp" #line 4 "library\\data_structure\\modint.hpp" #include #line 7 "library\\data_structure\\modint.hpp" #include using namespace std; #line 2 "library\\math\\extgcd.hpp" #line 4 "library\\math\\extgcd.hpp" #include #line 7 "library\\math\\extgcd.hpp" using namespace std; namespace asalib { namespace math { // Returns a pair (x, y) such that ax + by = c template constexpr optional> 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); } } // namespace math } // namespace asalib #line 11 "library\\data_structure\\modint.hpp" namespace asalib { namespace ds { class modint_base {}; template concept is_modint = is_base_of_v; template concept integral_or_modint = integral || is_modint; template* = nullptr> class static_modint: private modint_base { using mint = static_modint; public: constexpr static_modint(): _val(0) {}; template constexpr static_modint(T x): _val(((long long) x % mod + mod) % mod) {}; friend constexpr mint operator+(const mint& l, const mint& r) { return mint(l._val + r._val); } friend constexpr mint operator-(const mint& l, const mint& r) { return mint(l._val + mod - r._val); } friend constexpr mint operator*(const mint& l, const mint& r) { return mint((long long) l._val * r._val); } friend constexpr mint operator/(const mint& l, const mint& r) { return l * r.inv(); } constexpr mint operator+() const { return *this; } constexpr mint operator-() const { return 0 - *this; } constexpr mint& operator+=(const mint& other) { return *this = *this + other; } constexpr mint& operator-=(const mint& other) { return *this = *this - other; } constexpr mint& operator*=(const mint& other) { return *this = *this * other; } constexpr mint& operator/=(const mint& other) { return *this = *this / other; } constexpr mint& operator++() { return *this += 1; } constexpr mint& operator--() { return *this -= 1; } constexpr mint operator++(int) { mint res = *this; ++*this; return res; } constexpr mint operator--(int) { mint res = *this; --*this; return res; } friend constexpr bool operator==(const mint& l, const mint& r) { return l._val == r._val; } friend constexpr bool operator!=(const mint& l, const mint& r) { return !(l == r); } friend constexpr bool operator<(const mint& l, const mint& r) { return l._val < r._val; } template 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; } constexpr mint inv() const { if (is_prime_mod()) return pow(mod - 2); if (gcd(_val, mod) != 1) throw invalid_argument("Modular inverse does not exist"); return mint(math::extgcd(_val, mod, 1).value().first); } constexpr unsigned int val() const { return _val; } private: unsigned int _val; static constexpr bool is_prime_mod() { for (unsigned int i = 2; i * i <= mod; ++i) { if (mod % i == 0) return false; } return true; } }; template class dynamic_modint: private modint_base { using mint = dynamic_modint; public: constexpr dynamic_modint(): _val(0) {} template constexpr dynamic_modint(T x) { assert(_mod >= 1); _val = ((long long) x % _mod + _mod) % _mod; }; friend constexpr mint operator+(const mint& l, const mint& r) { return mint(l._val + r._val); } friend constexpr mint operator-(const mint& l, const mint& r) { return mint(l._val + l._mod - r._val); } friend constexpr mint operator*(const mint& l, const mint& r) { return mint((long long) l._val * r._val); } friend constexpr mint operator/(const mint& l, const mint& r) { return l * r.inv(); } constexpr mint operator+() const { return *this; } constexpr mint operator-() const { return 0 - *this; } constexpr mint& operator+=(const mint& other) { return *this = *this + other; } constexpr mint& operator-=(const mint& other) { return *this = *this - other; } constexpr mint& operator*=(const mint& other) { return *this = *this * other; } constexpr mint& operator/=(const mint& other) { return *this = *this / other; } constexpr mint& operator++() { return *this += 1; } constexpr mint& operator--() { return *this -= 1; } constexpr mint operator++(int) { mint res = *this; ++*this; return res; } constexpr mint operator--(int) { mint res = *this; --*this; return res; } friend constexpr bool operator==(const mint& l, const mint& r) { return l._val == r._val && l._mod == r._mod; } friend constexpr bool operator!=(const mint& l, const mint& r) { return !(l == r); } friend constexpr bool operator<(const mint& l, const mint& r) { return l._val < r._val; } template 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; } constexpr mint inv() const { if (gcd(_val, _mod) != 1) throw invalid_argument("Modular inverse does not exist"); return mint(asalib::math::extgcd(_val, _mod, 1).value().first); } constexpr unsigned int val() const { return _val; } constexpr static unsigned int mod() { return _mod; } constexpr static void set_mod(unsigned int mod) { assert(mod >= 1); _mod = mod; } private: unsigned int _val; static inline unsigned int _mod; }; } // namespace ds } // namespace asalib #line 7 "library\\data_structure\\matrix.hpp" namespace asalib { namespace ds { namespace internal { template concept matval = integral_or_modint || floating_point; } template 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(n_row * n_col) {}; constexpr Matrix(size_t n_row, size_t n_col, T x): _n_row(n_row), _n_col(n_col), _data(n_row * n_col, x) {}; // constexpr T& operator[](size_t i, size_t j) { return _data[i * _n_col + j]; } // constexpr const T& operator[](size_t i, size_t j) const { return _data[i * _n_col + j]; } // 使えないっぽいので at で代用 constexpr inline T& at(size_t i, size_t j) { return _data[i * _n_col + j]; } constexpr T at(size_t i, size_t j) const { return _data[i * _n_col + j]; } constexpr valarray row(size_t i) const { return valarray(_data[slice(i * _n_col, _n_col, 1)]); } constexpr valarray col(size_t j) const { return valarray(_data[slice(j, _n_row, _n_col)]); } constexpr Matrix operator+=(const T& x) { _data += x; return *this; } constexpr Matrix operator-=(const T& x) { _data -= x; return *this; } constexpr Matrix operator*=(const T& x) { _data *= x; return *this; } constexpr Matrix operator/=(const T& x) { _data /= x; return *this; } constexpr Matrix operator%=(const T& x) { _data %= x; return *this; } constexpr Matrix operator+(const T& x) const { return Matrix(*this) += x; } constexpr Matrix operator-(const T& x) const { return Matrix(*this) -= x; } constexpr Matrix operator*(const T& x) const { return Matrix(*this) *= x; } constexpr Matrix operator/(const T& x) const { return Matrix(*this) /= x; } constexpr Matrix operator%(const T& x) const { return Matrix(*this) %= x; } constexpr Matrix operator+=(const Matrix& x) { assert(_n_row == x._n_row); assert(_n_col == x._n_col); _data += x._data; return *this; } constexpr Matrix operator-=(const Matrix& x) { assert(_n_row == x._n_row); assert(_n_col == x._n_col); _data -= x._data; return *this; } 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 j = 0; j < x._n_col; ++j) { res.at(i, j) = (this->row(i) * x.col(j)).sum(); } } return *this = res; } constexpr Matrix operator+(const Matrix& x) const { return Matrix(*this) += x; } constexpr Matrix operator-(const Matrix& x) const { return Matrix(*this) -= x; } constexpr Matrix operator*(const Matrix& x) const { return Matrix(*this) *= x; } constexpr bool operator==(const Matrix& x) const { return _n_row == x._n_row && _n_col == x._n_col && _data == x._data; } constexpr bool operator!=(const Matrix& x) const { return !(*this == x); } constexpr bool operator<(const Matrix& x) const { return _data < x._data; } constexpr const Matrix transpose() const { Matrix res(_n_col, _n_row); for (size_t i = 0; i < _n_row; ++i) res._data[slice(i, _n_col, _n_row)] = _data[slice(i * _n_col, _n_col, 1)]; return res; } template constexpr Matrix pow(U x) { 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; } constexpr static Matrix I(size_t n) { Matrix res(n, n); res._data[std::slice(0, n, n + 1)] = 1; return res; } constexpr size_t n_row() const { return _n_row; } constexpr size_t n_col() const { return _n_col; } private: size_t _n_row, _n_col; valarray _data; }; } // namespace ds } // namespace asalib #line 8 "main.cpp" #define PROBLEM "https://yukicoder.me/problems/no/2441" int main() { cin.tie(nullptr)->sync_with_stdio(false); asalib::ds::Matrix a(2, 2); rep(i, 2) rep(j, 2) cin >> a.at(i, j); auto ans = a.pow(3); rep(i, 2) { rep(j, 2) cout << ans.at(i, j) << " \n"[j == 1]; } return 0; }