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;
#define IO ios_base::sync_with_stdio(false)
#define ll  long long
ll a[300300], b[302000], fc[300000];
vector<ll>v;

ll f(ll n, ll b, ll mod)
{
    ll aa, ans=1;
    if(!b) return 1;
    if(b%2) ans=n;
    aa = f(n,b/2,mod);
    return ((aa*aa)%mod*ans)%mod;
}
int main()
{
    IO;
    ll i, j=1, k = 0, mod = 1e9+7, m, mx, n, l = 1, p, t, h, kk=0, cnt=0;
    cin>>n>>m>>k;  p = n*m; fc[0]=1;

    for(i=1; i<=p; i++) fc[i]=(fc[i-1]*i)%mod;
    for(i=1; i<=n; i++){
        for(j=1; j<=m; j++){
            l = (n-i)*((j*(j-1))/2+((m-j)*(m-j+1))/2)+m*((n-i)*(n-i+1))/2+((m-j)*(m-j+1))/2;
            cnt=(cnt+l)%mod;
        }
    }
    l = (fc[p-2]*f((fc[p-k]*fc[k-2])%mod,mod-2,mod))%mod;
    cout<<(l*cnt)%mod<<endl;
    return 0;
}
