#include /** * @title modint * @docs mint.md */ template class ModInt{ public: constexpr static uint32_t MOD = M; uint64_t val; constexpr ModInt(): val(0){} constexpr ModInt(int64_t n){ if(n >= M) val = n % M; else if(n < 0) val = n % M + M; else val = n; } inline constexpr auto operator+(const ModInt &a) const {return ModInt(val + a.val);} inline constexpr auto operator-(const ModInt &a) const {return ModInt(val - a.val);} inline constexpr auto operator*(const ModInt &a) const {return ModInt(val * a.val);} inline constexpr auto operator/(const ModInt &a) const {return ModInt(val * a.inv().val);} inline constexpr auto& operator=(const ModInt &a){val = a.val; return *this;} inline constexpr auto& operator+=(const ModInt &a){if((val += a.val) >= M) val -= M; return *this;} inline constexpr auto& operator-=(const ModInt &a){if(val < a.val) val += M; val -= a.val; return *this;} inline constexpr auto& operator*=(const ModInt &a){(val *= a.val) %= M; return *this;} inline constexpr auto& operator/=(const ModInt &a){(val *= a.inv().val) %= M; return *this;} inline constexpr bool operator==(const ModInt &a) const {return val == a.val;} inline constexpr bool operator!=(const ModInt &a) const {return val != a.val;} inline constexpr auto& operator++(){*this += 1; return *this;} inline constexpr auto& operator--(){*this -= 1; return *this;} inline constexpr auto operator++(int){auto t = *this; *this += 1; return t;} inline constexpr auto operator--(int){auto t = *this; *this -= 1; return t;} inline constexpr static ModInt power(int64_t n, int64_t p){ if(p < 0) return power(n, -p).inv(); int64_t ret = 1, e = n % M; for(; p; (e *= e) %= M, p >>= 1) if(p & 1) (ret *= e) %= M; return ret; } inline constexpr static ModInt inv(int64_t a){ int64_t b = M, u = 1, v = 0; while(b){ int64_t t = a / b; a -= t * b; std::swap(a,b); u -= t * v; std::swap(u,v); } u %= M; if(u < 0) u += M; return u; } inline constexpr static auto frac(int64_t a, int64_t b){return ModInt(a) / ModInt(b);} inline constexpr auto power(int64_t p) const {return power(val, p);} inline constexpr auto inv() const {return inv(val);} friend inline constexpr auto operator-(const ModInt &a){return ModInt(-a.val);} friend inline constexpr auto operator+(int64_t a, const ModInt &b){return ModInt(a) + b;} friend inline constexpr auto operator-(int64_t a, const ModInt &b){return ModInt(a) - b;} friend inline constexpr auto operator*(int64_t a, const ModInt &b){return ModInt(a) * b;} friend inline constexpr auto operator/(int64_t a, const ModInt &b){return ModInt(a) / b;} friend std::istream& operator>>(std::istream &s, ModInt &a){s >> a.val; return s;} friend std::ostream& operator<<(std::ostream &s, const ModInt &a){s << a.val; return s;} template inline static auto div(){ static auto value = inv(N); return value; } explicit operator int32_t() const noexcept {return val;} explicit operator int64_t() const noexcept {return val;} }; /** * @title 正方行列 (コンパイル時固定サイズ) * @docs square_matrix_const_size.md */ template struct SquareMatrixConst{ using value_type = T; std::array,N> matrix; SquareMatrixConst(){ for(size_t i = 0; i < N; ++i) for(size_t j = 0; j < N; ++j) matrix[i][j] = 0; } SquareMatrixConst(const T &val){ for(size_t i = 0; i < N; ++i) matrix[i].fill(val); } SquareMatrixConst(std::initializer_list> list){ int i = 0; for(auto it1 = list.begin(); it1 != list.end(); ++it1, ++i){ int j = 0; for(auto it2 = it1->begin(); it2 != it1->end(); ++it2, ++j){ matrix[i][j] = *it2; } } } bool operator==(const SquareMatrixConst &val) const {return matrix == val.matrix;} bool operator!=(const SquareMatrixConst &val) const {return !(*this == val);} auto& operator=(const SquareMatrixConst &val){ this->matrix = val.matrix; return *this; } auto& operator+=(const SquareMatrixConst &val){ for(int i = 0; i < N; ++i) for(int j = 0; j < N; ++j) matrix[i][j] = matrix[i][j] + val[i][j]; return *this; } auto& operator-=(const SquareMatrixConst &val){ for(int i = 0; i < N; ++i) for(int j = 0; j < N; ++j) matrix[i][j] = matrix[i][j] - val[i][j]; return *this; } auto& operator*=(const SquareMatrixConst &val){ std::array,N> temp = {}; for(int i = 0; i < N; ++i) for(int j = 0; j < N; ++j) for(int k = 0; k < N; ++k) temp[i][j] = temp[i][j] + matrix[i][k] * val[k][j]; std::swap(matrix, temp); return *this; } inline const auto& operator[](size_t i) const {return matrix[i];} inline auto& operator[](size_t i){return matrix[i];} inline int size() const {return N;} static auto make_unit(){ SquareMatrixConst ret; for(size_t i = 0; i < N; ++i) ret[i][i] = 1; return ret; } friend auto operator+(const SquareMatrixConst &a, const SquareMatrixConst &b){auto ret = a; ret += b; return ret;} friend auto operator-(const SquareMatrixConst &a, const SquareMatrixConst &b){auto ret = a; ret -= b; return ret;} friend auto operator*(const SquareMatrixConst &a, const SquareMatrixConst &b){auto ret = a; ret *= b; return ret;} }; /** * @title 行列累乗 * @docs power.md */ template M power(M a, uint64_t p){ if(p == 0) return M::make_unit(); if(p == 1) return a; M temp = power(a, p >> 1); auto ret = temp * temp; if(p & 1) ret *= a; return ret; } /** * @docs show_matrix.md */ template void show_matrix(const M &m, int w = 10){ #ifdef DEBUG const int N = m.size(); std::cerr << "⎛" << std::string((w+1)*N, ' ') << "⎞" << std::endl; for(int i = 0; i < N; ++i){ std::cerr << "⎜"; for(int j = 0; j < N; ++j) std::cerr << std::setw(w) << m[i][j] << " "; std::cerr << "⎟"; std::cerr << std::endl; } std::cerr << "⎝" << std::string((w+1)*N, ' ') << "⎠" << std::endl; #endif } using mint = ModInt<1000000007>; using Mat = SquareMatrixConst; int main(){ int64_t N; while(std::cin >> N){ Mat m = { {mint::frac(1, 6), mint::frac(1, 6), mint::frac(1, 6), mint::frac(1, 6), mint::frac(1, 6), mint::frac(1, 6)}, {1, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0}, {0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 1, 0} }; m = power(m, N); //show_matrix(m); std::cout << m[0][0] << "\n"; } return 0; }