#include #include #include using namespace atcoder; using mint = modint1000000007; using namespace std; #define rep(i,n) for (int i = 0; i < (n); ++i) #define Inf 1000000000 template struct matrix{ F0 func0; F1 func1; vector> value; int height,width; T init_value0,init_value1; matrix(vector> X,F0 f0,F1 f1,T iv0,T iv1):func0(f0),func1(f1){ height = X.size(); width = X[0].size(); value = X; init_value0 = iv0,init_value1 = iv1; } matrix(int h,int w,F0 f0,F1 f1,T iv0,T iv1):func0(f0),func1(f1){ vector> d(h,vector(w,iv0)); height = h,width = w; value = d; init_value0 = iv0,init_value1 = iv1; } void set_1(){ for(int i=0;i R(height,another.width,func0,func1,init_value0,init_value1); for(int i=0;i R(height,width,func0,func1,init_value0,init_value1); R.set_1(); auto temp = *this; while(cnt!=0LL){ if(cnt%2==1){ R *= temp; } temp *= temp; cnt/=2; } return R; } }; int main(){ int C,N,M; cin>>C>>N>>M; vector> A(4,vector(4,0)); mint p = mint(C).inv(); A[0][0] = p; A[0][3] = p; rep(i,2)A[i*2+1][i*2] = 1; A[2][2] = p; A[2][1] = p * (C-1); A[2][3] = p * (C-2); /* rep(i,3){ rep(j,3){ if(i==j){ A[i*2][i*2] = p; } else{ A[i*2][j*2+1] = p; } } A[i*2+1][i*2] = 1; } */ auto f0 = [](mint a,mint b){ return a+b; }; auto f1 = [](mint a,mint b){ return a*b; }; matrix AA(A,f0,f1,0,1); vector> B(4,vector(4,0)); B[0][0] = 1; matrix BB(B,f0,f1,0,1); auto X = AA; X = X.beki(N); X *= BB; mint ans = X.value[0][0].val(); ans = 1-ans; ans = ans.pow(M); ans = 1-ans; cout<