We have a grid of squares with N rows and M columns. Let (i, j) denote the square at the i-th row from the top and j-th column from the left. We will choose K of the squares and put a piece on each of them.

If we place the K pieces on squares (x_1, y_1), (x_2, y_2), ..., and (x_K, y_K), the cost of this arrangement is computed as:

\sum_{i=1}^{K-1} \sum_{j=i+1}^K (|x_i - x_j| + |y_i - y_j|)

Find the sum of the costs of all possible arrangements of the pieces. Since this value can be tremendous, print it modulo 10^9+7.

We consider two arrangements of the pieces different if and only if there is a square that contains a piece in one of the arrangements but not in the other.

Constraints

* 2 \leq N \times M \leq 2 \times 10^5
* 2 \leq K \leq N \times M
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N M K


Output

Print the sum of the costs of all possible arrangements of the pieces, modulo 10^9+7.

Examples

Input

2 2 2


Output

8


Input

4 5 4


Output

87210


Input

100 100 5000


Output

817260251
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int mod=1e9+7;
ll m,n,k;
ll ksm(int x,int k)
{
	if(k==1) return x;
	ll ans=ksm(x,k/2);
	ans=(ans*ans)%mod;
	if(k%2) ans=ans*x%mod;
	return ans;
}
int main()
{
	scanf("%d%d%d",&n,&m,&k);
	ll i,j;
	ll cnt=0,cnt2=0,s=0,ans=0;;
	cnt=n*n;
	cnt%=mod;
	for(i=1;i<=m;i++) 
	s=(s+i*(m-i))%mod;
	cnt=(cnt*s)%mod;
	
	cnt2=m*m;
	cnt2%=mod;
	s=0;
	for(i=1;i<=n;i++)
	s=(s+i*(n-i))%mod;
	cnt2=(s*cnt2)%mod;
	
	ans=(cnt+cnt2)%mod;
	ll p=n*m-2;
	for(i=p;i>p-k+2;i--)
	ans=(ans*(i%mod))%mod;
	
	ll q=1;
	for(i=1;i<=k-2;i++) q=(q*(i%mod))%mod;
	
	q=ksm(q,mod-2);
	ans=ans*q%mod;
	cout<<ans;
	return 0;
 } 