#include "bits/stdc++.h" using namespace std; using ll = long long; using pii = pair; using pll = pair; using vi = vector; using vl = vector; using vvi = vector; using vvl = vector; const ll INF = 1LL << 60; const ll MOD = 1000000007; template bool chmax(T &a, const T &b) { return (a < b) ? (a = b, 1) : 0; } template bool chmin(T &a, const T &b) { return (b < a) ? (a = b, 1) : 0; } template void print(const C &c, std::ostream &os = std::cout) { std::copy(std::begin(c), std::end(c), std::ostream_iterator(os, " ")); os << std::endl; } // mod int struct // original : https://github.com/beet-aizu/library/blob/master/mod/mint.cpp struct mint { ll v; ll mod; mint() : v(0) {} mint(signed v, ll mod = MOD) : v(v), mod(mod) {} mint(ll t, ll mod = MOD) : mod(mod) { v = t % mod; if (v < 0) v += mod; } mint pow(ll k) { mint res(1), tmp(v); while (k) { if (k & 1) res *= tmp; tmp *= tmp; k >>= 1; } return res; } static mint add_identity() { return mint(0); } static mint mul_identity() { return mint(1); } mint inv() { return pow(mod - 2); } mint &operator+=(mint a) { v += a.v; if (v >= mod) v -= mod; return *this; } mint &operator-=(mint a) { v += mod - a.v; if (v >= mod) v -= mod; return *this; } mint &operator*=(mint a) { v = 1LL * v * a.v % mod; return *this; } mint &operator/=(mint a) { return (*this) *= a.inv(); } mint operator+(mint a) const { return mint(v) += a; }; mint operator-(mint a) const { return mint(v) -= a; }; mint operator*(mint a) const { return mint(v) *= a; }; mint operator/(mint a) const { return mint(v) /= a; }; mint operator-() const { return v ? mint(mod - v) : mint(v); } bool operator==(const mint a) const { return v == a.v; } bool operator!=(const mint a) const { return v != a.v; } bool operator<(const mint a) const { return v < a.v; } // find x s.t. a^x = b static ll log(ll a, ll b) { const ll sq = 40000; unordered_map dp; dp.reserve(sq); mint res(1); for (int r = 0; r < sq; r++) { if (!dp.count(res.v)) dp[res.v] = r; res *= a; } mint p = mint(a).inv().pow(sq); res = b; for (int q = 0; q <= MOD / sq + 1; q++) { if (dp.count(res.v)) { ll idx = q * sq + dp[res.v]; if (idx > 0) return idx; } res *= p; } assert(0); return ll(-1); } static mint comb(long long n, int k) { mint num(1), dom(1); for (int i = 0; i < k; i++) { num *= mint(n - i); dom *= mint(i + 1); } return num / dom; } }; ostream &operator<<(ostream &os, mint m) { os << m.v; return os; } template struct SquareMatrix { using arr = array; using mat = array; mat dat; SquareMatrix() { for (size_t i = 0; i < N; i++) for (size_t j = 0; j < N; j++) dat[i][j] = R::add_identity(); } SquareMatrix &operator=(const SquareMatrix &a) { dat = a.dat; return (*this); } bool operator==(const SquareMatrix &a) const { return dat == a.dat; } size_t size() const { return N; }; arr &operator[](size_t k) { return dat[k]; }; const arr &operator[](size_t k) const { return dat[k]; }; static SquareMatrix add_identity() { return SquareMatrix(); } static SquareMatrix mul_identity() { SquareMatrix res; for (size_t i = 0; i < N; i++) res[i][i] = R::mul_identity(); return res; } SquareMatrix operator*(const SquareMatrix &B) const { SquareMatrix res; for (size_t i = 0; i < N; i++) for (size_t j = 0; j < N; j++) for (size_t k = 0; k < N; k++) res[i][j] = res[i][j] + (dat[i][k] * B[k][j]); return res; } SquareMatrix operator+(const SquareMatrix &B) const { SquareMatrix res; for (size_t i = 0; i < N; i++) for (size_t j = 0; j < N; j++) res[i][j] = dat[i][j] + B[i][j]; return res; } SquareMatrix pow(long long n) const { SquareMatrix a = *this, res = mul_identity(); while (n) { if (n & 1) res = res * a; a = a * a; n >>= 1; } return res; } }; int main() { ll a, b, n; cin >> a >> b >> n; if (n == 0) { cout << 0 << "\n"; return 0; } else if (n == 1) { cout << 1 << "\n"; return 0; } SquareMatrix<2, mint> arr; arr[0][1] = 1; arr[1][0] = b; arr[1][1] = a; auto arrpow = arr.pow(n - 1); mint ret = arrpow[1][1]; cout << ret << "\n"; return 0; }