#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #define endl codeforces #define ALL(v) std::begin(v), std::end(v) #define ALLR(v) std::rbegin(v), std::rend(v) using ll = std::int64_t; using ull = std::uint64_t; using pii = std::pair; using tii = std::tuple; using pll = std::pair; using tll = std::tuple; using size_type = ssize_t; template using vec = std::vector; template using vvec = vec>; template const T& var_min(const T &t) { return t; } template const T& var_max(const T &t) { return t; } template const T& var_min(const T &t, const Tail&... tail) { return std::min(t, var_min(tail...)); } template const T& var_max(const T &t, const Tail&... tail) { return std::max(t, var_max(tail...)); } template void chmin(T &t, const Tail&... tail) { t = var_min(t, tail...); } template void chmax(T &t, const Tail&... tail) { t = var_max(t, tail...); } template struct multi_dim_array { using type = std::array::type, Head>; }; template struct multi_dim_array { using type = std::array; }; template using mdarray = typename multi_dim_array::type; template void fill_seq(T &t, F f, Args... args) { if constexpr (std::is_invocable::value) { t = f(args...); } else { for (size_type i = 0; i < t.size(); i++) fill_seq(t[i], f, args..., i); } } template vec make_v(size_type sz) { return vec(sz); } template auto make_v(size_type hs, Tail&&... ts) { auto v = std::move(make_v(std::forward(ts)...)); return vec(hs, v); } namespace init__ { struct InitIO { InitIO() { std::cin.tie(nullptr); std::ios_base::sync_with_stdio(false); std::cout << std::fixed << std::setprecision(30); } } init_io; } template T ceil_pow2(T bound) { T ret = 1; while (ret < bound) ret *= 2; return ret; } template T ceil_div(T a, T b) { return a / b + !!(a % b); } namespace math { template constexpr T mul_id_ele() { if constexpr (std::is_fundamental::value) { return T(1); } else { return T::mul_id_ele(); } } template constexpr T add_id_ele() { if constexpr (std::is_fundamental::value) { return T(0); } else { return T::add_id_ele(); } } template constexpr T pow(const T &n, ll k) { T ret = mul_id_ele(); T cur = n; while (k) { if (k & 1) ret *= cur; cur *= cur; k /= 2; } return ret; } template typename std::enable_if::value, T>::type gcd(T a, T b) { return b ? gcd(a % b, b) : a; } } namespace math { template struct Modint { constexpr Modint(ll x) noexcept : x((Mod + x % static_cast(Mod)) % Mod) { } constexpr Modint() noexcept : Modint(0) { } constexpr static Modint add_id_ele() { return Modint(0); } constexpr static Modint mul_id_ele() { return Modint(1); } constexpr ll value() const noexcept { return static_cast(x); } constexpr Modint& operator+=(const Modint &oth) noexcept { x += oth.value(); if (Mod <= x) x -= Mod; return *this; } constexpr Modint& operator-=(const Modint &oth) noexcept { x += Mod - oth.value(); if (Mod <= x) x -= Mod; return *this; } constexpr Modint& operator*=(const Modint &oth) noexcept { x *= oth.value(); x %= Mod; return *this; } constexpr Modint& operator/=(const Modint &oth) noexcept { x *= oth.inv().value(); x %= Mod; return *this; } constexpr Modint operator+(const Modint &oth) const noexcept { return Modint(x) += oth; } constexpr Modint operator-(const Modint &oth) const noexcept { return Modint(x) -= oth; } constexpr Modint operator*(const Modint &oth) const noexcept { return Modint(x) *= oth; } constexpr Modint operator/(const Modint &oth) const noexcept { return Modint(x) /= oth; } constexpr Modint operator-() const noexcept { return Modint((x != 0) * (Mod - x)); } constexpr bool operator==(const Modint &oth) const noexcept { return value() == oth.value(); } template constexpr typename std::enable_if::value, const Modint&>::type operator=(T t) noexcept { (*this) = Modint(std::forward(t)); return *this; } constexpr Modint inv() const noexcept { return ::math::pow(*this, Mod - 2); } constexpr ull mod() const noexcept { return Mod; } private: ull x; }; template Modint inv(Modint m) { return m.inv(); } template std::istream& operator>>(std::istream &is, Modint &m) { ll v; is >> v; m = v; return is; } template std::ostream& operator<<(std::ostream &os, Modint m) { os << m.value(); return os; } } namespace math { template struct Matrix : mdarray { using mdarray::mdarray; constexpr Matrix& operator+=(const Matrix &rhs) { for (size_type i = 0; i < M; i++) for (size_type j = 0; j < N; j++) (*this)[i][j] += rhs[i][j]; } constexpr Matrix operator+(const Matrix &rhs) const { return Matrix(*this) += rhs; } template constexpr Matrix operator*(const Matrix &rhs) const { Matrix ret; for (size_type i = 0; i < M; i++) for (size_type j = 0; j < L; j++) ret[i][j] = T(); for (size_type i = 0; i < M; i++) { for (size_type j = 0; j < N; j++) { for (size_type k = 0; k < L; k++) { ret[i][k] += (*this)[i][j] * rhs[j][k]; } } } return ret; } constexpr Matrix& operator*=(const T &c) { for (size_type i = 0; i < M; i++) for (size_type j = 0; j < N; j++) (*this)[i][j] *= c; return *this; } constexpr Matrix operator*(const T &c) const { return Matrix(*this) *= c; } size_type row() const noexcept { return M; } size_type col() const noexcept { return N; } static Matrix add_id_ele() { Matrix ret; fill_seq(ret, [&](size_type, size_type) { return T(0); }); return ret; } static Matrix mul_id_ele() { static_assert(M == N, "Matrix must be square."); Matrix ret; fill_seq(ret, [&](size_type i, size_type j) { return i == j ? T(1) : T(0); // TODO : is this correct ?? }); return ret; } }; template std::ostream& operator<<(std::ostream &os, const Matrix &mat) { for (size_type i = 0; i < M; i++) { os << (i == 0 ? "[ " : " "); for (size_type j = 0; j < N; j++) os << mat[i][j] << ", "; os << (i + 1 == M ? " ]" : "\n"); } return os; } } constexpr ll mod = 1e9 + 7; using mint = math::Modint; using matrix_t = math::Matrix; int main() { mint a, b; ll n; std::cin >> a >> b >> n; auto mat = matrix_t::add_id_ele(); mat[0][0] = a; mat[0][1] = 1; mat[1][0] = b; mat[1][1] = a; auto res = matrix_t::mul_id_ele(), cur = mat; while (n) { if (n & 1) res = cur * res; cur = cur * cur; n /= 2; } auto ans = res[1][1]; ans *= 2; std::cout << ans << '\n'; return 0; }