#include #include #include #include #include #include #include #include #include static const int MOD = 1000000007; using ll = long long; using u32 = unsigned; using u64 = unsigned long long; using namespace std; template constexpr T INF = ::numeric_limits::max() / 32 * 15 + 208; template struct modint { u32 val; public: static modint raw(int v) { modint x; x.val = v; return x; } modint() : val(0) {} template modint(T v) { ll x = (ll)(v%(ll)(M)); if (x < 0) x += M; val = u32(x); } modint(bool v) { val = ((unsigned int)(v) % M); } modint& operator++() { val++; if (val == M) val = 0; return *this; } modint& operator--() { if (val == 0) val = M; val--; return *this; } modint operator++(int) { modint result = *this; ++*this; return result; } modint operator--(int) { modint result = *this; --*this; return result; } modint& operator+=(const modint& b) { val += b.val; if (val >= M) val -= M; return *this; } modint& operator-=(const modint& b) { val -= b.val; if (val >= M) val += M; return *this; } modint& operator*=(const modint& b) { u64 z = val; z *= b.val; val = (u32)(z % M); return *this; } modint& operator/=(const modint& b) { return *this = *this * b.inv(); } modint operator+() const { return *this; } modint operator-() const { return modint() - *this; } modint pow(long long n) const { modint x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; } modint inv() const { return pow(M-2); } friend modint operator+(const modint& a, const modint& b) { return modint(a) += b; } friend modint operator-(const modint& a, const modint& b) { return modint(a) -= b; } friend modint operator*(const modint& a, const modint& b) { return modint(a) *= b; } friend modint operator/(const modint& a, const modint& b) { return modint(a) /= b; } friend bool operator==(const modint& a, const modint& b) { return a.val == b.val; } friend bool operator!=(const modint& a, const modint& b) { return a.val != b.val; } }; using mint = modint; template struct SquareMatrix { using T = typename H::T; using ar = array; using mat = array; mat A; SquareMatrix() = default; static SquareMatrix I(){ SquareMatrix X; for (int i = 0; i < SIZE; ++i) { for (int j = 0; j < SIZE; ++j) { if(i == j) X[i][j] = H::one(); else X[i][j] = H::zero(); } } return X; } static SquareMatrix O(){ SquareMatrix X; for (auto &&i : X.A) fill(i.begin(),i.end(), H::zero()); return X; } friend ar operator*=(ar &x, const SquareMatrix &Y) { ar ans; fill(ans.begin(),ans.end(), H::zero()); for (int i = 0; i < SIZE; ++i) { for (int j = 0; j < SIZE; ++j) { H::add(ans[j], H::mul(x[i], Y[i][j])); } } x.swap(ans); return x; } friend ar operator*(ar x, const SquareMatrix &Y) { return x *= Y; } inline const ar &operator[](int k) const{ return (A.at(k)); } inline ar &operator[](int k) { return (A.at(k)); } SquareMatrix &operator+= (const SquareMatrix &B){ for (int i = 0; i < SIZE; ++i) { for (int j = 0; j < SIZE; ++j) { H::add((*this)[i][j], B[i][j]); } } return (*this); } SquareMatrix &operator-= (const SquareMatrix &B){ for (int i = 0; i < SIZE; ++i) { for (int j = 0; j < SIZE; ++j) { H::add((*this)[i][j], -B[i][j]); } } return (*this); } SquareMatrix &operator*=(const SquareMatrix &B) { SquareMatrix C = O(); for (int i = 0; i < SIZE; ++i) { for (int k = 0; k < SIZE; ++k) { for (int j = 0; j < SIZE; ++j) { H::add(C[i][j], H::mul((*this)[i][k], B[k][j])); } } } A.swap(C.A); return (*this); } SquareMatrix pow(ll n) const { SquareMatrix a = (*this), res = I(); while(n > 0){ if(n & 1) res *= a; a *= a; n >>= 1; } return res; } SquareMatrix operator+(const SquareMatrix &B) const {return SquareMatrix(*this) += B;} SquareMatrix operator-(const SquareMatrix &B) const {return SquareMatrix(*this) -= B;} SquareMatrix operator*(const SquareMatrix &B) const {return SquareMatrix(*this) *= B;} }; struct SemiRing { using T = mint; static inline T mul(T x, T y){ return x * y; } static inline void add(T &x, T y){ x += y; } static inline T one(){ return 1; } static inline T zero(){ return 0; } }; using ar = array; using mat = SquareMatrix; int main() { int a, b; ll n; cin >> a >> b >> n; ar x; x[0] = 1; x[1] = 0; mat A; A[0][0] = a, A[1][0] = b; A[0][1] = 1; A[1][1] = a; A = A.pow(n); cout << ((x*A)[0]*2).val << "\n"; return 0; }