#include #define ll long long #define INF 1000000005 #define MOD 1000000007 #define EPS 1e-10 #define rep(i,n) for(int i=0;i<(int)(n);++i) #define rrep(i,n) for(int i=(int)(n)-1;i>=0;--i) #define srep(i,s,t) for(int i=(int)(s);i<(int)(t);++i) #define each(a,b) for(auto& (a): (b)) #define all(v) (v).begin(),(v).end() #define len(v) (int)(v).size() #define zip(v) sort(all(v)),v.erase(unique(all(v)),v.end()) #define cmx(x,y) x=max(x,y) #define cmn(x,y) x=min(x,y) #define fi first #define se second #define pb push_back #define show(x) cout<<#x<<" = "<<(x)< P; typedef pair pll; typedef vector vi; typedef vector vvi; typedef vector vl; typedef vector vvl; typedef vector vd; typedef vector

vp; typedef vector vs; const int MAX_N = 100005; // powかmod_powかはその都度変更する // 係数の順番に注意する!!! // A[n] = 3*A[n-1]+2*A[n-2] とかなら a は {2,3} となる template class mat : public vector > { private: int r,c; //行,列 public: int row() const { return r; } int column() const { return c; } mat(int n,int m,T val = 0){ this->r = n,this->c = m; rep(i,n){ this->push_back(vector(m,val)); } } mat operator+(const mat& another){ if(this->r != another.r && this->c != another.c){ cout << "足し算失敗(サイズ不一致)" << endl; exit(1); } mat X(this->r,this->c); rep(i,this->r){ rep(j,this->c){ X[i][j] = (*this)[i][j] + another[i][j]; } } return X; } mat operator+(const T val){ mat X(this->r,this->c); rep(i,this->r){ rep(j,this->c){ X[i][j] = (*this)[i][j] + val; } } return X; } mat operator-(const mat& another){ if(this->r != another.r && this->c != another.c){ cout << "引き算失敗(サイズ不一致)" << endl; exit(1); } mat X(this->r,this->c); rep(i,this->r){ rep(j,this->c){ X[i][j] = (*this)[i][j] - another[i][j]; } } return X; } mat operator-(const T val){ mat X(this->r,this->c); rep(i,this->r){ rep(j,this->c){ X[i][j] = (*this)[i][j] - val; } } return X; } vector operator*(const vector& another){ if(this->c != (int)another.size()){ cout << "掛け算失敗(サイズ不一致)" << endl; exit(1); } vector vec(this->r,0); rep(i,this->r){ rep(j,this->c){ vec[i] += (*this)[i][j] * another[j]; } } return vec; } mat operator*(const mat& another){ if(this->c != another.r){ cout << "掛け算失敗(サイズ不一致)" << endl; exit(1); } mat X(this->r,another.c); rep(i,this->r){ rep(k,this->c){ rep(j,another.c){ X[i][j] += (*this)[i][k]*another[k][j]; } } } return X; } mat operator-(){ mat X(this->r,this->c); rep(i,this->r){ rep(j,this->c){ X[i][j] = -(*this)[i][j]; } } return X; } void print(){ rep(i,this->r){ rep(j,(this->c)-1){ cout << (*this)[i][j] << ","; } cout << (*this)[i][(this->c)-1] << endl; } } }; template mat pow(mat A,ll cnt) { if(A.row() != A.column()){ cout << "累乗不可" << endl; } int n = A.row(); mat B(n,n); rep(i,n){ B[i][i] = 1; } while(cnt>0){ if(cnt & 1){ B = B*A; } A = A*A; cnt >>= 1; } return B; } template mat mod_mul(mat& A,mat& B) { if(A.column() != B.row()){ cout << "掛け算失敗(サイズ不一致)" << endl; exit(1); } mat X(A.row(),B.column()); rep(i,A.row()){ rep(k,A.column()){ rep(j,B.column()){ X[i][j] = (X[i][j] + A[i][k]*B[k][j]) % MOD; } } } return X; } template mat mod_pow(mat A,ll cnt) { if(A.row() != A.column()){ cout << "累乗不可" << endl; } int n = A.row(); mat B(n,n); rep(i,n){ B[i][i] = 1; } while(cnt>0){ if(cnt & 1){ B = mod_mul(B,A); } A = mod_mul(A,A); cnt >>= 1; } return B; } // 第1引数 : A[n] = a[0] + a[1] * A[n-k] + a[2] * A[n-k+1] + ... + a[k] * A[n-1] // 第2引数 : A[0] = x[0], A[1] = x[1], ... , A[k-1] = x[k-1] template T solve(vector& a, vector& x, ll n) { int k = (int)a.size() - 1; if(n < k){ return x[n]; } mat A(k+1,k+1); rep(i,k+1){ A[0][i] = a[k-i]; } rep(i,k-1){ A[i+1][i] = 1; } A[k][k] = 1; mat B = mod_pow(A,n-k+1); T res = 0; rep(i,k){ res = (res + B[0][i]*x[k-1-i]%MOD) % MOD; } res = (res + B[0][k]) % MOD; return res; } int main() { cin.tie(0); ios::sync_with_stdio(false); ll b,c,d; cin >> b >> c >> d; b %= MOD, c %= MOD, d; vl a = {b*c%MOD,c}, x = {0}; cout << solve(a,x,d) << "\n"; return 0; }