#ifdef LOCAL111 #define _GLIBCXX_DEBUG #else #define NDEBUG #endif #define _USE_MATH_DEFINES #ifndef _GLIBCXX_NO_ASSERT #include #endif #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #if __cplusplus >= 201103L #include #include #include #include #include #include #include #include #endif // C++ #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 #include #include #if __cplusplus >= 201103L #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #endif const int INF = 1e9; using namespace std; template ostream& operator<< (ostream& os, const pair& p) { os << '(' << p.first << ' ' << p.second << ')'; return os; } #define endl '\n' #define ALL(a) (a).begin(),(a).end() #define SZ(a) int((a).size()) #define FOR(i,a,b) for(int i=(a);i<(b);++i) #define RFOR(i,a,b) for (int i=(b)-1;i>=(a);i--) #define REP(i,n) FOR(i,0,n) #define RREP(i,n) for (int i=(n)-1;i>=0;i--) #ifdef LOCAL111 #define DEBUG(x) cout<<#x<<": "<<(x)< void dpite(T a, T b){ for(T ite = a; ite != b; ite++) cout << (ite == a ? "" : " ") << *ite; cout << endl;} #else #define DEBUG(x) true template void dpite(T a, T b){ return; } #endif #define F first #define S second #define SNP string::npos #define WRC(hoge) cout << "Case #" << (hoge)+1 << ": " template void pite(T a, T b){ for(T ite = a; ite != b; ite++) cout << (ite == a ? "" : " ") << *ite; cout << endl;} template bool chmax(T& a, T b){if(a < b){a = b; return true;} return false;} template bool chmin(T& a, T b){if(a > b){a = b; return true;} return false;} typedef long long int LL; typedef unsigned long long ULL; typedef pair P; void ios_init(){ //cout.setf(ios::fixed); //cout.precision(12); #ifdef LOCAL111 return; #endif ios::sync_with_stdio(false); cin.tie(0); } #define EPS 1e-9 //library template class Matrix { public: vector > v; int n,m; Matrix(int n){ this->n = this->m = n; v.resize(n,vector(n,0)); } Matrix(int n, int m){ this -> n = n; this -> m = m; v.resize(n,vector(m,0)); } size_t size() const { return v.size(); } int row() const { return n; } int col() const { return m; } Matrix operator+ (Matrix x) const { Matrix res(n,m); for(int i = 0; i < n; i++){ for(int j = 0; j < m; j++){ res.v[i][j] = x.v[i][j]+v[i][j]; } } return res; } Matrix operator-(Matrix x) const { Matrix res(n,m); for(int i = 0; i < n; i++){ for(int j = 0; j < m; j++){ res.v[i][j] = v[i][j]-x.v[i][j]; } } } Matrix operator*(Matrix x) const { Matrix res(n,x.m); for(int i = 0; i < n; i++){ for(int j = 0; j < x.m; j++){ for(int k = 0; k < m; k++){ res.v[i][j] += v[i][k]*x.v[k][j]; } } } return res; } Matrix operator-() const { Matrix res = *this; for(int i = 0; i < (int)v.size(); ++i) { for(int j = 0; j < (int)v[i].size(); ++j) { res [i][j] *= -1; } } return res; } vector operator*(vector x) const { assert(x.size() == v.size()); vector res(v.size()); for(int i = 0; i < n; i++){ T tmp = 0; for(int j = 0; j < m; j++){ tmp += v[i][j]*x[j]; } res[i] = tmp; } return res; } Matrix pow(long long x) const { assert(n == m); Matrix m = (*this); Matrix res(n); for(int i = 0; i < n; i++) res[i][i] = 1; while(x != 0) { if(x&1) { res = res*m; } m = m*m; x >>= 1; } return res; } vector& operator[](int x){ return v[x]; } const vector& operator[](int x) const { return v[x]; } Matrix inverse() const{ assert(n == m); Matrix res(n); for(int i = 0; i < n; ++i) { res[i][i] = 1; } // vector> swap_log; Matrix mat = *this; for(int k = 0; k < n; ++k) { T max_val = abs(mat[k][k]); int max_point = k; for(int i = k+1; i < n; ++i) { if(max_val < abs(mat[i][k])){ max_val = abs(mat[i][k]); max_point = i; } } swap(mat[k],mat[max_point]); swap(res[k],res[max_point]); // swap_log.emplace_back(k,max_point); for(int i = k+1; i < n; ++i) { T m = mat[i][k]/mat[k][k]; for(int j = 0; j < n; ++j) { mat[i][j] -= m*mat[k][j]; res[i][j] -= m*res[k][j]; } } } for(int k = n-1; k >= 0; --k) { for(int i = 0; i < k; ++i) { T m = mat[i][k]/mat[k][k]; for(int j = 0; j < n; ++j) { // mat[i][j] -= mat[k][j]*m; res[i][j] -= res[k][j]*m; } } } for(int i = 0; i < n; ++i) { for(int j = 0; j < n; ++j) { res[i][j] /= mat[i][i]; } } // for(auto&& e : swap_log) { // swap(res[e.first],res[e.second]); // } return res; } T det() const { Matrix mat = *this; T res = 1; for(int k = 0; k < n; ++k) { T max_val = abs(mat[k][k]); int max_point = k; for(int i = k+1; i < n; ++i) { if(max_val < abs(mat[i][k])){ max_val = abs(mat[i][k]); max_point = i; } } swap(mat[k],mat[max_point]); if(k != max_point) res *= -1; for(int i = k+1; i < n; ++i) { T m = mat[i][k]/mat[k][k]; for(int j = 0; j < n; ++j) { mat[i][j] -= m*mat[k][j]; } } } for(int i = 0; i < n; ++i) { res *= mat[i][i]; } return res; } pair> getMaxEigenvalue(int iterNum = 10) const { assert(n == m); vector xk_(n, 1); xk_ = (*this).pow(iterNum)*xk_; auto xk = (*this)*xk_; T xk_xk = 0, xk_xk_ = 0; for(int i = 0; i < n; i++) { xk_xk += xk[i]*xk[i]; xk_xk_ += xk[i]*xk_[i]; } T xkAbs = sqrt(xk_xk); auto res = xk; for(auto&& e : res) { e /= xkAbs; } return { xk_xk/xk_xk_, res }; } void debug() const { for(auto&& ee : v) { for(auto&& e : ee) { cout << e << ' '; } cout << endl; } cout << endl; } }; template Matrix companion_pow(const Matrix& A, long long m) { assert(A.col() == A.row()); int n = A.col(); Matrix u(1, n), Ak = A; u[0][n-1] = 1; while(m > 0) { if(m&1) { u = u*Ak; } Matrix a(1, n); for(int i = 0; i < n; ++i) { a[0][i] = Ak[n-1][i]; } a = a*Ak; for(int i = n-1; i >= 0; --i) { for(int j = 0; j < n; ++j) { Ak[i][j] = a[0][j]; } auto a00 = a[0][0]; for(int j = 0; j < n-1; ++j) { a[0][j] = a[0][j+1]+A[0][j]*a00; } a[0][n-1] = A[0][n-1]*a00; } m >>= 1; } Matrix res(n); for(int i = n-1; i >= 0; --i) { for(int j = 0; j < n; ++j) { res[i][j] = u[0][j]; } auto u00 = u[0][0]; for(int j = 0; j < n-1; ++j) { u[0][j] = u[0][j+1]+A[0][j]*u00; } u[0][n-1] = A[0][n-1]*u00; } return res; } //libary template class ModInt { public: const static long long mod = MOD; long long x; ModInt() { x = 0; } ModInt(long long x) { x %= mod; this->x = x < 0 ? x+mod : x; } int get() const { return (int)x; } ModInt &operator+=(ModInt that) { if((x += that.get()) >= mod) x -= mod; return *this; } ModInt &operator-=(ModInt that) { if((x += mod-that.get()) >= mod) x -= mod; return *this; } ModInt &operator*=(ModInt that) { x = x*that.get()%mod; return *this; } ModInt &operator/=(ModInt that) { return *this *= that.inverse(); } ModInt operator+(ModInt that) const { return ModInt(*this) += that; } ModInt operator-(ModInt that) const { return ModInt(*this) -= that; } ModInt operator*(ModInt that) const { return ModInt(*this) *= that; } ModInt operator/(ModInt that) const { return ModInt(*this) /= that; } ModInt inverse() const { using std::swap; long long a = x, b = mod, u = 1, v = 0; while(b) { long long t = a/b; a -= t*b; swap(a,b); u -= t*v; swap(u,v); } return ModInt(u); } ModInt pow(int n) const { ModInt b = *this; ModInt res = 1; while(n != 0) { if(n&1){ res *= b; } b *= b; n >>= 1; } return res; } bool operator==(ModInt that) const { return x == that.get(); } bool operator!=(ModInt that) const { return x != that.get(); } ModInt operator-() const { return x == 0 ? 0 : ModInt(mod-x); } }; template ostream& operator<< (ostream& os, const ModInt& m) { os << m.get(); return os; } template istream& operator>> (istream& is, ModInt& m){ long long n; is >> n; m = n; return is;} typedef ModInt<1000000007> mint; typedef double Num; typedef vector Vec; typedef vector Mat; int mrank(Mat A) { int n = A.size(); int m = A[0].size(); int ret = 0; for(int i = 0; i < n; i ++) { //DEBUG(i); int pivot = i; for(int j = i+1; j < n; j ++) if(abs(A[pivot][i]) < abs(A[j][i])) pivot = j; swap(A[i], A[pivot]); if(abs(A[i][i]) < EPS) continue; Num r = Num(1) / A[i][i]; for(int j = i+1; j < n; j ++) { Num u = A[j][i] * r; for(int k = n-1; k >= i; k --) A[j][k] -= u * A[i][k]; } } for(int i = 0; i < n; i++){ if(abs(A[i][m-1]) > EPS) ret = i; } /*REP(i,n) pite(ALL(A[i])); cout << endl;*/ return ret; } //libary int main() { ios_init(); LL b, c, d; while(cin >> b >> c >> d) { Matrix m(2, 2); m[0][0] = c; m[0][1] = b; m[1][1] = 1; auto po = m.pow(d); REP(i, 2) dpite(ALL(po[i])); auto ans = (po*vector({b, 1}))[0]; cout << ans-mint(b) << endl; } return 0; }