#include<bits/stdc++.h>
#define del(a,i) memset(a,i,sizeof(a))
#define ll long long
#define inl inline
#define il inl void
#define it inl int
#define ill inl ll
#define re register
#define ri re int
#define rl re ll
#define mid ((l+r)>>1)
#define lowbit(x) (x&(-x))
#define INF 0x3f3f3f3f
using namespace std;
template<class T>il read(T &x){
	int f=1;char k=getchar();x=0;
	for(;k>'9'||k<'0';k=getchar()) if(k=='-') f=-1;
	for(;k>='0'&&k<='9';k=getchar()) x=x*10+k-'0';
	x*=f;
}
template<class T>il _print(T x){
	if(x>=10) _print(x/10);
	putchar(x%10+'0');
}
template<class T>il print(T x){
	if(x<0) putchar('-'),x=-x;
	_print(x);
}
ll mul(ll a,ll b,ll mod){long double c=1.;return (a*b-(ll)(c*a*b/mod)*mod)%mod;}
it qpow(int x,int k,int mod){
	int res=1,bas=x;
	while(k){
		if(k&1) res=1ll*res*bas%mod;
		bas=1ll*bas*bas%mod,k>>=1;
	}
	return res;
}
const int N = 2e5+5,mod = 1e9+7;
it add(int x,int y){return x+y>=mod?x+y-mod:x+y;}
it mul(int x,int y){return 1ll*x*y%mod;}
il inc(int &x,int y){x=add(x,y);}
int n,m,k,ans,fac[N],ifac[N];
it C(int n,int m){return mul(mul(ifac[n-m],ifac[m]),fac[n]);}
int main(){
//	freopen(".in","r",stdin);
//	freopen(".out","w",stdout);
	read(n),read(m),read(k),fac[0]=1;
	for(ri i=1;i<=n*m;++i) fac[i]=mul(fac[i-1],i);
	ifac[n*m]=qpow(fac[n*m],mod-2,mod);
	for(ri i=n*m-1;i>=0;--i) ifac[i]=mul(ifac[i+1],i+1);
	for(ri i=1;i<=n-1;++i) inc(ans,mul(mul(mul(m,m),n-i),i));
	for(ri i=1;i<=m-1;++i) inc(ans,mul(mul(mul(n,n),m-i),i));
	print(mul(ans,C(n*m-2,k-2)));
	return 0;
}
#include<bits/stdc++.h>
#define int long long
#define F first
#define S second
#define P pair
#define FOR(i,a,b) for(int i=a;i<=b;i++)
#define V vector
#define RE return
#define ALL(a) a.begin(),a.end()
#define MP make_pair
#define PB push_back
#define PF push_front
#define FILL(a,b) memset(a,b,sizeof(a))
using namespace std;
int mod=1e9+7; 
int inv[200005],finv[200005],f[200005];
void C(){
	f[0]=1;finv[0]=1;finv[1]=1;f[1]=1;inv[1]=1;
	FOR(i,2,200000){
		f[i]=f[i-1]*i%mod;
		inv[i]=mod-inv[mod%i]*(mod/i)%mod;
		finv[i]=finv[i-1]*inv[i]%mod; 
	}
}
signed main(){
	ios::sync_with_stdio(0);
    cin.tie(0);
	int n,m,k;
	cin>>n>>m>>k;
	C();
	int sum,ans=0,t=n*m;
	FOR(i,1,n){
		FOR(j,1,m){
			sum=0;
			int t1=i-1,t2=j-1;
			sum=sum+t1*(t1+1)/2%mod*m+t2*(t2+1)/2%mod*n;sum=sum%mod;
			t1=n-t1-1;t2=m-t2-1;
			sum=sum+t1*(t1+1)/2%mod*m+t2*(t2+1)/2%mod*n;sum=sum%mod;
			sum=sum*inv[t-1]%mod*f[t-1]%mod*finv[t-k]%mod*finv[k-2]%mod;
			ans=(ans+sum)%mod;
		}
	} 
	cout<<ans*inv[2]%mod;
	RE 0;
}


