#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 "my-library\\library\\data-structure\\matrix.hpp" #line 4 "my-library\\library\\data-structure\\matrix.hpp" #include #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" #include using namespace std; namespace asalib::_internal { class modint_base {}; template concept is_modint = is_base_of_v; } #line 7 "my-library\\library\\_internal\\types.hpp" namespace asalib::_internal { template concept integral_like = integral || is_modint; template concept floating_like = floating_point; template concept numeric_like = integral_like || floating_like; template T plus(T a, T b) { return a + b; } template T minus(T a, T b) { return a - b; } template T zero() { return 0; } } #line 10 "my-library\\library\\data-structure\\matrix.hpp" namespace asalib::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(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(x, n_col)); }; constexpr T& at(size_t i, size_t j) { assert(i < _n_row); assert(j < _n_col); return _data[i][j]; } constexpr T at(size_t i, size_t j) const { assert(i < _n_row); assert(j < _n_col); return _data[i][j]; } 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 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; } 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 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 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; } 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; } 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; public: constexpr T determinant() const; template<_internal::numeric_like U> 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 #line 6 "my-library\\library\\math\\extgcd.hpp" using namespace std; namespace asalib::math { 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); } } #line 12 "my-library\\library\\data-structure\\modint.hpp" namespace asalib::ds { template requires(mod >= 1) class static_modint: _internal::modint_base { using mint = static_modint; using uint = unsigned int; using ll = long long; using ull = unsigned long long; public: constexpr static_modint(): _val(0) {}; template constexpr static_modint(const T& x) { if constexpr (is_signed_v) { ll y = x % static_cast(mod); if (y < 0) y += mod; _val = y; } else { _val = x % mod; } } friend constexpr mint operator+(const mint& l, const mint& r) { return mint(l) += r; } friend constexpr mint operator-(const mint& l, const mint& r) { return mint(l) -= r; } friend constexpr mint operator*(const mint& l, const mint& r) { return mint(l) *= r; } friend constexpr mint operator/(const mint& l, const mint& r) { return mint(l) /= r; } constexpr mint operator+() const { return *this; } constexpr mint operator-() const { return 0 - *this; } constexpr mint& operator+=(const mint& other) { _val += other._val; if (_val >= mod) _val -= mod; return *this; } constexpr mint& operator-=(const mint& other) { _val -= other._val; if (_val >= mod) _val += mod; return *this; } constexpr mint& operator*=(const mint& other) { ull z = _val; z *= other._val; _val = z % mod; return *this; } constexpr mint& operator/=(const mint& other) { return *this = *this * other.inv(); } constexpr mint& operator++() { _val++; if (_val == mod) _val = 0; return *this; } constexpr mint& operator--() { if (_val == 0) _val = mod; _val--; return *this; } constexpr mint operator++(int) { mint res = *this; ++*this; return res; } constexpr mint operator--(int) { mint res = *this; --*this; return res; } constexpr bool operator==(const mint& r) const { return _val == r._val; } constexpr bool operator!=(const mint& r) const { return _val != r._val; } constexpr bool operator<(const mint& r) const { return _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 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(_val, mod, 1).value().first); } } constexpr unsigned int val() const { return _val; } private: uint _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: _internal::modint_base { using mint = dynamic_modint; using uint = unsigned int; using ll = long long; using ull = unsigned long long; public: constexpr dynamic_modint(): _val(0) {} template constexpr dynamic_modint(const T& x) { assert(_mod >= 1); if constexpr (is_signed_v) { ll y = x % static_cast(_mod); if (y < 0) y += _mod; _val = y; } else { _val = x % _mod; } }; friend constexpr auto operator+(const mint& l, const mint& r) -> mint { return mint(l) += r; } friend constexpr mint operator-(const mint& l, const mint& r) { return mint(l) -= r; } friend constexpr mint operator*(const mint& l, const mint& r) { return mint(l) *= r; } friend constexpr mint operator/(const mint& l, const mint& r) { return mint(l) /= r; } constexpr mint operator+() const { return *this; } constexpr mint operator-() const { return 0 - *this; } constexpr mint& operator+=(const mint& other) { _val += other._val; if (_val >= _mod) _val -= _mod; return *this; } constexpr mint& operator-=(const mint& other) { _val -= other._val; if (_val >= _mod) _val += _mod; return *this; } constexpr mint& operator*=(const mint& other) { ull z = _val; z *= other._val; _val = z % _mod; return *this; } constexpr mint& operator/=(const mint& other) { return *this = *this * other.inv(); } constexpr mint& operator++() { _val++; if (_val == _mod) _val = 0; return *this; } constexpr mint& operator--() { if (_val == 0) _val = _mod; _val--; return *this; } constexpr mint operator++(int) { mint res = *this; ++*this; return res; } constexpr mint operator--(int) { mint res = *this; --*this; return res; } constexpr bool operator==(const mint& r) const { return _val == r._val; } constexpr bool operator!=(const mint& r) const { return _val != r._val; } constexpr bool operator<(const mint& r) const { return _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(math::extgcd(_val, _mod, 1).value().first); } constexpr uint val() const { return _val; } constexpr static uint mod() { return _mod; } constexpr static void set_mod(const uint mod) { assert(mod >= 1); _mod = mod; } private: uint _val; static inline uint _mod; }; } #line 9 "main.cpp" using mint = asalib::ds::static_modint<1000000007>; int main() { cin.tie(nullptr)->sync_with_stdio(false); ll a, b, c, d, e, n; cin >> a >> b >> c >> d >> e >> n; if (n == 0) { cout << mint(a).val() << '\n'; return 0; } asalib::matrix::Matrix M(5, 5); M.at(0, 0) = 1, M.at(0, 1) = c, M.at(0, 2) = d, M.at(0, 3) = 0, M.at(0, 4) = e; M.at(1, 0) = 0, M.at(1, 1) = c, M.at(1, 2) = d, M.at(1, 3) = 0, M.at(1, 4) = e; M.at(2, 0) = 0, M.at(2, 1) = 1, M.at(2, 2) = 0, M.at(2, 3) = 0, M.at(2, 4) = 0; M.at(3, 0) = 0, M.at(3, 1) = 0, M.at(3, 2) = 1, M.at(3, 3) = 0, M.at(3, 4) = 0; M.at(4, 0) = 0, M.at(4, 1) = 0, M.at(4, 2) = 0, M.at(4, 3) = 0, M.at(4, 4) = 1; asalib::matrix::Matrix init(5, 1); init.at(0, 0) = a + b, init.at(1, 0) = b, init.at(2, 0) = a, init.at(3, 0) = 0, init.at(4, 0) = 1; cout << (M.pow(n - 1) * init).at(0, 0).val() << '\n'; return 0; }