#include #include template struct ModInt { using lint = long long; int val; // constructor ModInt(lint v = 0) : val(v % MOD) { if (val < 0) val += MOD; }; // unary operator ModInt operator+() const { return ModInt(val); } ModInt operator-() const { return ModInt(MOD - val); } ModInt inv() const { return this->pow(MOD - 2); } // arithmetic ModInt operator+(const ModInt& x) const { return ModInt(*this) += x; } ModInt operator-(const ModInt& x) const { return ModInt(*this) -= x; } ModInt operator*(const ModInt& x) const { return ModInt(*this) *= x; } ModInt operator/(const ModInt& x) const { return ModInt(*this) /= x; } ModInt pow(lint n) const { auto x = ModInt(1); auto b = *this; while (n > 0) { if (n & 1) x *= b; n >>= 1; b *= b; } return x; } // compound assignment ModInt& operator+=(const ModInt& x) { if ((val += x.val) >= MOD) val -= MOD; return *this; } ModInt& operator-=(const ModInt& x) { if ((val -= x.val) < 0) val += MOD; return *this; } ModInt& operator*=(const ModInt& x) { val = lint(val) * x.val % MOD; return *this; } ModInt& operator/=(const ModInt& x) { return *this *= x.inv(); } // compare bool operator==(const ModInt& b) const { return val == b.val; } bool operator!=(const ModInt& b) const { return val != b.val; } bool operator<(const ModInt& b) const { return val < b.val; } bool operator<=(const ModInt& b) const { return val <= b.val; } bool operator>(const ModInt& b) const { return val > b.val; } bool operator>=(const ModInt& b) const { return val >= b.val; } // I/O friend std::istream& operator>>(std::istream& is, ModInt& x) noexcept { lint v; is >> v; x = v; return is; } friend std::ostream& operator<<(std::ostream& os, const ModInt& x) noexcept { return os << x.val; } }; template struct Vector { using V = std::array; V vec; // constructor Vector() = default; Vector(T val) { vec.fill(val); } // getter T& operator[](int i) { return vec[i]; } T operator[](int i) const { return vec[i]; } typename V::iterator begin() { return vec.begin(); } typename V::iterator end() { return vec.end(); } // arithmetic Vector operator+(const Vector& v) const { return Matrix(*this) += v; } Vector operator-(const Vector& v) const { return Matrix(*this) -= v; } T operator*(const Vector& v) const { T ret(0); for (int i = 0; i < D; ++i) ret += vec[i] * v[i]; return ret; } // compound assignment Vector& operator+=(const Vector& v) { for (int i = 0; i < D; ++i) vec[i] += v[i]; return *this; } Vector& operator-=(const Vector& v) { for (int i = 0; i < D; ++i) vec[i] -= v[i]; return *this; } }; template struct Matrix { using M = std::array, D>; M mat; // constructor Matrix() = default; Matrix(T val) { for (auto& v : mat) v.fill(val); } static Matrix id() { Matrix m; for (int i = 0; i < D; ++i) m[i][i] = 1; return m; } // getter std::array& operator[](int i) { return mat[i]; } std::array operator[](int i) const { return mat[i]; } typename M::iterator begin() { return mat.begin(); } typename M::iterator end() { return mat.end(); } // arithmetic Matrix operator+(const Matrix& m) const { return Matrix(*this) += m; } Matrix operator-(const Matrix& m) const { return Matrix(*this) -= m; } Matrix operator*(const Matrix& m) const { return Matrix(*this) *= m; } template Matrix pow(U k) { Matrix ret = id(); Matrix a = *this; while (k > 0) { if (k & 1) ret *= a; a *= a; k >>= 1; } return ret; } // compound assignment Matrix& operator+=(const Matrix& m) { for (int i = 0; i < D; ++i) { for (int j = 0; j < D; ++j) { mat[i][j] += m[i][j]; } } return *this; } Matrix& operator-=(const Matrix& m) { for (int i = 0; i < D; ++i) { for (int j = 0; j < D; ++j) { mat[i][j] -= m[i][j]; } } return *this; } Matrix& operator*=(const Matrix& m) { M nmat; for (int i = 0; i < D; ++i) { for (int j = 0; j < D; ++j) { for (int k = 0; k < D; ++k) { nmat[i][j] += mat[i][k] * m[k][j]; } } } mat = nmat; return *this; } // arithmetic with vector using Vec = Vector; Vec operator*(const Vec& v) { Vec ret; for (int i = 0; i < D; ++i) { for (int j = 0; j < D; ++j) { ret[i] += mat[i][j] * v[j]; } } return ret; } }; constexpr int MOD = 1000000007; using mint = ModInt; using Mat = Matrix; void solve() { mint a, b; int n; std::cin >> a >> b >> n; Mat m; m[0][0] = a, m[0][1] = b, m[1][0] = 1; std::cout << (m.pow(n))[1][0] << "\n"; } int main() { std::cin.tie(nullptr); std::ios::sync_with_stdio(false); solve(); return 0; }