#include #include #include #include #include #define _USE_MATH_DEFINES #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; #define FOR(i,m,n) for(int i=(m);i<(n);++i) #define REP(i,n) FOR(i,0,n) #define ALL(v) (v).begin(),(v).end() const int INF = 0x3f3f3f3f; const long long LINF = 0x3f3f3f3f3f3f3f3fLL; const double EPS = 1e-8; const int MOD = 1000000007; // 998244353; const int dy[] = {1, 0, -1, 0}, dx[] = {0, -1, 0, 1}; /*-------------------------------------------------*/ int mod = MOD; struct ModInt { unsigned val; ModInt(): val(0) {} ModInt(long long x) : val(x >= 0 ? x % mod : x % mod + mod) {} ModInt pow(long long exponent) { ModInt tmp = *this, res = 1; while (exponent > 0) { if (exponent & 1) res *= tmp; tmp *= tmp; exponent >>= 1; } return res; } ModInt &operator+=(const ModInt &rhs) { if((val += rhs.val) >= mod) val -= mod; return *this; } ModInt &operator-=(const ModInt &rhs) { if((val += mod - rhs.val) >= mod) val -= mod; return *this; } ModInt &operator*=(const ModInt &rhs) { val = (unsigned long long)val * rhs.val % mod; return *this; } ModInt &operator/=(const ModInt &rhs) { return *this *= rhs.inv(); } bool operator==(const ModInt &rhs) const { return val == rhs.val; } bool operator!=(const ModInt &rhs) const { return val != rhs.val; } bool operator<(const ModInt &rhs) const { return val < rhs.val; } bool operator<=(const ModInt &rhs) const { return val <= rhs.val; } bool operator>(const ModInt &rhs) const { return val > rhs.val; } bool operator>=(const ModInt &rhs) const { return val >= rhs.val; } ModInt operator-() const { return ModInt(-val); } ModInt operator+(const ModInt &rhs) const { return ModInt(*this) += rhs; } ModInt operator-(const ModInt &rhs) const { return ModInt(*this) -= rhs; } ModInt operator*(const ModInt &rhs) const { return ModInt(*this) *= rhs; } ModInt operator/(const ModInt &rhs) const { return ModInt(*this) /= rhs; } friend ostream &operator<<(ostream &os, const ModInt &rhs) { return os << rhs.val; } friend istream &operator>>(istream &is, ModInt &rhs) { long long x; is >> x; rhs = ModInt(x); return is; } private: ModInt inv() const { // if (__gcd((int)val, mod) != 1) assert(false); unsigned a = val, b = mod; int x = 1, y = 0; while (b) { unsigned tmp = a / b; swap(a -= tmp * b, b); swap(x -= tmp * y, y); } return ModInt(x); } }; ModInt abs(const ModInt &x) { return x.val; } struct Combinatorics { Combinatorics(int MAX = 5000000) { MAX <<= 1; fact.resize(MAX + 1); fact_inv.resize(MAX + 1); fact[0] = 1; FOR(i, 1, MAX + 1) fact[i] = fact[i - 1] * i; fact_inv[MAX] = ModInt(1) / fact[MAX]; for (int i = MAX; i > 0; --i) fact_inv[i - 1] = fact_inv[i] * i; } ModInt nCk(int n, int k) { if (n < 0 || n < k || k < 0) return ModInt(0); return fact[n] * fact_inv[k] * fact_inv[n - k]; } ModInt nPk(int n, int k) { if (n < 0 || n < k || k < 0) return ModInt(0); return fact[n] * fact_inv[n - k]; } ModInt nHk(int n, int k) { if (n < 0 || k < 0) return ModInt(0); return (k == 0 ? ModInt(1) : nCk(n + k - 1, k)); } private: vector fact, fact_inv; }; template struct Matrix { Matrix(int m, int n, T val = 0) : dat(m, vector(n, val)) {} int height() const { return dat.size(); } int width() const { return dat.front().size(); } Matrix pow(long long exponent) { int n = height(); Matrix tmp = *this, res(n, n, 0); REP(i, n) res[i][i] = 1; while (exponent > 0) { if (exponent & 1) res *= tmp; tmp *= tmp; exponent >>= 1; } return res; } inline const vector &operator[](const int idx) const { return dat[idx]; } inline vector &operator[](const int idx) { return dat[idx]; } Matrix &operator=(const Matrix &rhs) { int m = rhs.height(), n = rhs.width(); dat.resize(m, vector(n)); REP(i, m) REP(j, n) dat[i][j] = rhs[i][j]; return *this; } Matrix &operator+=(const Matrix &rhs) { int m = height(), n = width(); REP(i, m) REP(j, n) dat[i][j] += rhs[i][j]; return *this; } Matrix &operator-=(const Matrix &rhs) { int m = height(), n = width(); REP(i, m) REP(j, n) dat[i][j] -= rhs[i][j]; return *this; } Matrix &operator*=(const Matrix &rhs) { int m = height(), n = rhs.width(), l = width(); vector > res(m, vector(n, 0)); REP(i, m) REP(j, n) { REP(k, l) res[i][j] += dat[i][k] * rhs[k][j]; } swap(dat, res); return *this; } Matrix operator+(const Matrix &rhs) const { return Matrix(*this) += rhs; } Matrix operator-(const Matrix &rhs) const { return Matrix(*this) -= rhs; } Matrix operator*(const Matrix &rhs) const { return Matrix(*this) *= rhs; } private: vector > dat; }; int main() { cin.tie(nullptr); ios::sync_with_stdio(false); // freopen("input.txt", "r", stdin); int a, b, n; cin >> a >> b >> n; if (n <= 1) { cout << n << '\n'; return 0; } Matrix m(2, 2), r(2, 1); m[0][0] = a; m[0][1] = b; r[0][0] = 1; m[1][0] = 1; m[1][1] = 0; r[1][0] = 0; auto ans = m.pow(n - 1) * r; cout << ans[0][0] << '\n'; return 0; }