#include using namespace std; typedef signed long long ll; #define _P(...) (void)printf(__VA_ARGS__) #define FOR(x,to) for(x=0;x<(to);x++) #define FORR(x,arr) for(auto& x:arr) #define FORR2(x,y,arr) for(auto& [x,y]:arr) #define ALL(a) (a.begin()),(a.end()) #define ZERO(a) memset(a,0,sizeof(a)) #define MINUS(a) memset(a,0xff,sizeof(a)) template bool chmax(T &a, const T &b) { if(a bool chmin(T &a, const T &b) { if(a>b){a=b;return 1;}return 0;} //------------------------------------------------------- int N; ll M,K; const ll mo=1000000007; ll comb(ll N_, ll C_) { const int NUM_=400001; static ll fact[NUM_+1],factr[NUM_+1],inv[NUM_+1]; if (fact[0]==0) { inv[1]=fact[0]=factr[0]=1; for (int i=2;i<=NUM_;++i) inv[i] = inv[mo % i] * (mo - mo / i) % mo; for (int i=1;i<=NUM_;++i) fact[i]=fact[i-1]*i%mo, factr[i]=factr[i-1]*inv[i]%mo; } if(C_<0 || C_>N_) return 0; return factr[C_]*fact[N_]%mo*factr[N_-C_]%mo; } const int MAT=2; struct Mat { ll v[MAT][MAT]; Mat(){ZERO(v);};}; Mat mulmat(Mat& a,Mat& b,int n=MAT) { ll mo2=4*mo*mo; int x,y,z; Mat r; FOR(x,n) FOR(y,n) r.v[x][y]=0; FOR(x,n) FOR(z,n) FOR(y,n) { r.v[x][y] += a.v[x][z]*b.v[z][y]; if(r.v[x][y]>mo2) r.v[x][y] -= mo2; } FOR(x,n) FOR(y,n) r.v[x][y]%=mo; return r; } Mat powmat(ll p,Mat a,int n=MAT) { int i,x,y; Mat r; FOR(x,n) FOR(y,n) r.v[x][y]=0; FOR(i,n) r.v[i][i]=1; while(p) { if(p%2) r=mulmat(r,a,n); a=mulmat(a,a,n); p>>=1; } return r; } void dfs(vector V,Mat& A,int K) { int ma=*max_element(ALL(V)); if(V.size()==6) { if(V[0]==V[3]) return; if(V[1]==V[4]) return; if(V[2]==V[5]) return; if(V[3]==V[4]) return; if(V[4]==V[5]) return; int x=V[0]==V[2]; int y=V[3]==V[5]; if(x) (A.v[y][x]+=comb(K-(ma+1),(ma+1)-2))%=mo; else (A.v[y][x]+=comb(K-(ma+1),(ma+1)-3))%=mo; } else { int i; FOR(i,ma+2) { V.push_back(i); dfs(V,A,K); V.pop_back(); } } } ll hoge(int K) { Mat A; ll ret; if(N==1) { A.v[0][0]=K-1; A=powmat(M-1,A); ret=K*A.v[0][0]%mo; } else if(N==2) { A.v[0][0]=((K-2)*(K-2)+K-1)%mo; A=powmat(M-1,A); ret=K*(K-1)%mo*A.v[0][0]%mo; } else { // XYZ->XYZ dfs({0,1,0},A,K); dfs({0,1,2},A,K); A=powmat(M-1,A); ll XYX=K*(K-1)%mo; ll XYZ=K*(K-1)%mo*(K-2)%mo; //cout<>N>>M>>K; ll ret=0; for(i=1;i<=K;i++) { ll a=hoge(i)*comb(K,i)%mo; //cout<