#include using namespace std; typedef long long ll; const int MOD = 1000000007; // 2x2行列の構造体 struct Matrix { ll a11, a12, a21, a22; Matrix(ll _a11=1, ll _a12=0, ll _a21=0, ll _a22=1) : a11(_a11), a12(_a12), a21(_a21), a22(_a22) {} // 行列の乗算 Matrix operator*(const Matrix& other) const { Matrix res; res.a11 = (a11 * other.a11 + a12 * other.a21) % MOD; res.a12 = (a11 * other.a12 + a12 * other.a22) % MOD; res.a21 = (a21 * other.a11 + a22 * other.a21) % MOD; res.a22 = (a21 * other.a12 + a22 * other.a22) % MOD; return res; } }; // 行列累乗の高速化 Matrix power_matrix(Matrix base, ll power){ Matrix result(1, 0, 0, 1); // 単位行列 while(power > 0){ if(power & 1){ result = result * base; } base = base * base; power >>=1; } return result; } int main(){ ios::sync_with_stdio(false); cin.tie(0); ll a, b, n; cin >> a >> b >> n; // n=0およびn=1の場合を個別に処理 if(n == 0){ cout << 2 % MOD; return 0; } if(n == 1){ ll s1 = (2 * (a % MOD)) % MOD; cout << s1; return 0; } // 2a mod MODを計算 ll two_a = (2 * (a % MOD)) % MOD; // (a^2 - b) mod MODを計算 ll a_sq_mod = (a % MOD) * (a % MOD) % MOD; ll a_sq_minus_b = (a_sq_mod - (b % MOD) + MOD) % MOD; // 遷移行列を定義 Matrix trans(two_a, (MOD - a_sq_minus_b) % MOD, 1, 0); // trans^(n-1)を計算 Matrix trans_n_minus_1 = power_matrix(trans, n-1); // 初期ベクトル [S(1), S(0)] = [2a, 2] ll S1 = two_a; ll S0 = 2 % MOD; // S(n) = trans^(n-1) * [S1, S0]^T を計算 ll Sn = (trans_n_minus_1.a11 * S1 + trans_n_minus_1.a12 * S0) % MOD; cout << Sn; }