#define _USE_MATH_DEFINES #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() using ll = long long; constexpr int INF = 0x3f3f3f3f; constexpr ll LINF = 0x3f3f3f3f3f3f3f3fLL; constexpr double EPS = 1e-8; constexpr int MOD = 1000000007; // constexpr int MOD = 998244353; constexpr int dy[] = {1, 0, -1, 0}, dx[] = {0, -1, 0, 1}; constexpr int dy8[] = {1, 1, 0, -1, -1, -1, 0, 1}, dx8[] = {0, -1, -1, -1, 0, 1, 1, 1}; template inline bool chmax(T &a, U b) { return a < b ? (a = b, true) : false; } template inline bool chmin(T &a, U b) { return a > b ? (a = b, true) : false; } struct IOSetup { IOSetup() { cin.tie(nullptr); ios_base::sync_with_stdio(false); cout << fixed << setprecision(20); } } iosetup; template struct MInt { unsigned val; MInt(): val(0) {} MInt(long long x) : val(x >= 0 ? x % MOD : x % MOD + MOD) {} static int get_mod() { return MOD; } static void set_mod(int divisor) { assert(divisor == MOD); } MInt pow(long long exponent) const { MInt tmp = *this, res = 1; while (exponent > 0) { if (exponent & 1) res *= tmp; tmp *= tmp; exponent >>= 1; } return res; } MInt &operator+=(const MInt &x) { if((val += x.val) >= MOD) val -= MOD; return *this; } MInt &operator-=(const MInt &x) { if((val += MOD - x.val) >= MOD) val -= MOD; return *this; } MInt &operator*=(const MInt &x) { val = static_cast(val) * x.val % MOD; return *this; } MInt &operator/=(const MInt &x) { // assert(std::__gcd(static_cast(x.val), MOD) == 1); unsigned a = x.val, b = MOD; int u = 1, v = 0; while (b) { unsigned tmp = a / b; std::swap(a -= tmp * b, b); std::swap(u -= tmp * v, v); } return *this *= u; } bool operator==(const MInt &x) const { return val == x.val; } bool operator!=(const MInt &x) const { return val != x.val; } bool operator<(const MInt &x) const { return val < x.val; } bool operator<=(const MInt &x) const { return val <= x.val; } bool operator>(const MInt &x) const { return val > x.val; } bool operator>=(const MInt &x) const { return val >= x.val; } MInt &operator++() { if (++val == MOD) val = 0; return *this; } MInt operator++(int) { MInt res = *this; ++*this; return res; } MInt &operator--() { val = (val == 0 ? MOD : val) - 1; return *this; } MInt operator--(int) { MInt res = *this; --*this; return res; } MInt operator+() const { return *this; } MInt operator-() const { return MInt(val ? MOD - val : 0); } MInt operator+(const MInt &x) const { return MInt(*this) += x; } MInt operator-(const MInt &x) const { return MInt(*this) -= x; } MInt operator*(const MInt &x) const { return MInt(*this) *= x; } MInt operator/(const MInt &x) const { return MInt(*this) /= x; } friend std::ostream &operator<<(std::ostream &os, const MInt &x) { return os << x.val; } friend std::istream &operator>>(std::istream &is, MInt &x) { long long val; is >> val; x = MInt(val); return is; } }; namespace std { template MInt abs(const MInt &x) { return x; } } template struct Combinatorics { using ModInt = MInt; int val; // "val!" and "mod" must be disjoint. std::vector fact, fact_inv, inv; Combinatorics(int val = 10000000) : val(val), fact(val + 1), fact_inv(val + 1), inv(val + 1) { fact[0] = 1; for (int i = 1; i <= val; ++i) fact[i] = fact[i - 1] * i; fact_inv[val] = ModInt(1) / fact[val]; for (int i = val; i > 0; --i) fact_inv[i - 1] = fact_inv[i] * i; for (int i = 1; i <= val; ++i) inv[i] = fact[i - 1] * fact_inv[i]; } ModInt nCk(int n, int k) const { if (n < 0 || n < k || k < 0) return 0; assert(n <= val && k <= val); return fact[n] * fact_inv[k] * fact_inv[n - k]; } ModInt nPk(int n, int k) const { if (n < 0 || n < k || k < 0) return 0; assert(n <= val); return fact[n] * fact_inv[n - k]; } ModInt nHk(int n, int k) const { if (n < 0 || k < 0) return 0; return k == 0 ? 1 : nCk(n + k - 1, k); } }; using ModInt = MInt; template struct Matrix { Matrix(int m, int n, T val = 0) : dat(m, std::vector(n, val)) {} int height() const { return dat.size(); } int width() const { return dat.front().size(); } Matrix pow(long long exponent) const { int n = height(); Matrix tmp = *this, res(n, n, 0); for (int i = 0; i < n; ++i) res[i][i] = 1; while (exponent > 0) { if (exponent & 1) res *= tmp; tmp *= tmp; exponent >>= 1; } return res; } inline const std::vector &operator[](const int idx) const { return dat[idx]; } inline std::vector &operator[](const int idx) { return dat[idx]; } Matrix &operator=(const Matrix &x) { int m = x.height(), n = x.width(); dat.resize(m, std::vector(n)); for (int i = 0; i < m; ++i) for (int j = 0; j < n; ++j) dat[i][j] = x[i][j]; return *this; } Matrix &operator+=(const Matrix &x) { int m = height(), n = width(); for (int i = 0; i < m; ++i) for (int j = 0; j < n; ++j) dat[i][j] += x[i][j]; return *this; } Matrix &operator-=(const Matrix &x) { int m = height(), n = width(); for (int i = 0; i < m; ++i) for (int j = 0; j < n; ++j) dat[i][j] -= x[i][j]; return *this; } Matrix &operator*=(const Matrix &x) { int m = height(), n = x.width(), l = width(); std::vector> res(m, std::vector(n, 0)); for (int i = 0; i < m; ++i) for (int j = 0; j < n; ++j) { for (int k = 0; k < l; ++k) res[i][j] += dat[i][k] * x[k][j]; } std::swap(dat, res); return *this; } Matrix operator+(const Matrix &x) const { return Matrix(*this) += x; } Matrix operator-(const Matrix &x) const { return Matrix(*this) -= x; } Matrix operator*(const Matrix &x) const { return Matrix(*this) *= x; } private: std::vector> dat; }; int main() { ll a, b, n; cin >> a >> b >> n; if (n == 0) { cout << 2 << '\n'; return 0; } Matrix m(2, 2), init(2, 1); m[0][0] = a * 2; m[0][1] = b - a * a; m[1][0] = 1; init[0][0] = a * 2; init[1][0] = 2; cout << (m.pow(n - 1) * init)[0][0] << '\n'; return 0; }