#include #include using namespace std; #include template struct combination{ vectorfac,ifac; combination(size_t N=0):fac(1,1),ifac(1,1) { make_table(N); } void make_table(size_t N) { if(fac.size()>N)return; size_t now=fac.size(); N=max(N,now*2); fac.resize(N+1); ifac.resize(N+1); for(size_t i=now;i<=N;i++)fac[i]=fac[i-1]*i; ifac[N]=1/fac[N]; for(size_t i=N;i-->now;)ifac[i]=ifac[i+1]*(i+1); } T factorial(size_t n) { make_table(n); return fac[n]; } T invfac(size_t n) { make_table(n); return ifac[n]; } T P(size_t n,size_t k) { if(nC; int N,M,K; int main() { cin>>N>>M>>K; int T=min(N,M); int n=N*M; mint V=1; for(int i=1;i<=K;i++)V*=mint::raw(i); for(int i=0;i<=K;i++)V/=mint::raw(n+i); mint ans=V*n; //mint ans=n*C.factorial(K)*C.factorial(n-1)*C.invfac(n+K); for(int c=1;c<=T;c++) { const mint coef=C.C(N,c)*C.C(M,c)*K; //x^c * (1-x)^(T-c) //ans+=C.factorial(c+K-1)*C.factorial(n-c)*C.invfac(n+K)*coef; ans+=V*coef; V*=mint::raw(K+c); V/=mint::raw(n-c); } cout<