#include #include #include #include #include #include #include #include #include #include #include #include #define debug_value(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << #x << "=" << x << endl; #define debug(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << x << endl; template inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; } template inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; } using namespace std; typedef long long ll; const ll MOD = 1000000007; class ModInt{ public: ll v; ModInt(ll _v = 0){ if(_v >= MOD) _v %= MOD; v = _v; } ModInt operator+(ll n){ return ModInt((v+n)%MOD); } ModInt operator-(ll n){ return ModInt((v-n+MOD)%MOD); } ModInt operator*(ll n){ if(n >= MOD) n %= MOD; return ModInt((v*n)%MOD); } ModInt operator/(ll n){ return ModInt((ModInt(n).inv()*v).v%MOD); } void operator+=(ll n){ v = (v+n)%MOD; } void operator-=(ll n){ v = (v-n+MOD)%MOD; } void operator*=(ll n){ v = (v*n+MOD)%MOD; } ModInt operator+(ModInt n){ return ModInt((v+n.v)%MOD); } ModInt operator-(ModInt n){ return ModInt((v-n.v+MOD)%MOD); } ModInt operator*(ModInt n){ return ModInt((v*n.v)%MOD); } ModInt operator/(ModInt n){ return ModInt((n.inv()*v).v%MOD); } void operator+=(ModInt n){ v = (v+n.v)%MOD; } void operator-=(ModInt n){ v = (v-n.v+MOD)%MOD; } void operator*=(ModInt n){ v = (v*n.v)%MOD; } void operator=(ModInt n){ v = n.v; } bool operator==(ModInt n){ return v == n.v; } bool operator!=(ModInt n){ return v != n.v; } void operator=(ll n){ v = n%MOD; } ModInt inv(){ if(v == 1) return ModInt(1); else return ModInt(MOD-ModInt(MOD%v).inv().v*(MOD/v)%MOD); } }; ostream& operator<<(ostream& os, const ModInt& m){ os << m.v; return os; } istream & operator >> (istream &in, ModInt &m){ in >> m.v; return in; } template struct matrix{ int n, m; vector> dat; matrix(int n_, int m_){ n = n_; m = m_; for(int i = 0; i < n; i++){ dat.push_back(vector(m)); } } vector& operator[](int x) { return dat[x]; } }; template bool prod(matrix a, matrix b, matrix &ans){ assert(a.m == b.n); for(int i = 0; i < a.n; i++){ for(int j = 0; j < b.m; j++){ ans.dat[i][j] = 0; for(int k = 0; k < b.n; k++){ ans.dat[i][j] += (a.dat[i][k]*b.dat[k][j]); } } } return true; } template void copy_mat(matrix a, matrix &b){ assert(a.n == b.n); assert(a.m == b.m); for(int i = 0; i < a.n; i++){ for(int j = 0; j < a.m; j++){ b.dat[i][j] = a.dat[i][j]; } } } template void pow_mat(matrix a, ll n, matrix &ans){ assert(n < ((ll)1<<61)); matrix buf(a.n, a.n); matrix tmp(a.n, a.n); copy_mat(a, tmp); for(int i = 0; i < a.n; i++) { for(int j = 0; j < a.n; j++){ ans.dat[i][j] = 0; } ans.dat[i][i] = 1; } for(int i = 0; i <= 60; i++){ ll m = (ll)1 << i; if(m&n){ prod(tmp, ans, buf); copy_mat(buf, ans); } prod(tmp, tmp, buf); copy_mat(buf, tmp); } } template void print_mat(matrix a){ for(int i = 0; i < a.n; i++){ for(int j = 0; j < a.m; j++){ cout << a.dat[i][j] << ' '; } cout << endl; } } template ostream& operator<<(ostream& os, const matrix& m){ print_mat(m); return os; } using mint = ModInt; int main(){ ios::sync_with_stdio(false); cin.tie(0); cout << setprecision(10) << fixed; ll a, b, n; cin >> a >> b >> n; ll s = 2*a, t = a*a-b; matrix m(2, 2), p(2, 2), u(2, 1), ans(2, 1); m[0][0] = s, m[0][1] = mint(MOD-t); m[1][0] = 1; u[0][0] = 2*a; u[1][0] = 2; pow_mat(m, n, p); prod(p, u, ans); cout << ans[1][0] << endl; }