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<iostream>
#include<cstdio>
#include<algorithm>
#include<cstring>
#include<cmath>
using namespace std;
#define int long long
const int mod = 1e9 + 7;
inline int fpow(int n, int p){
    int ans = 1, base = n;
    while(p){
        if(p & 1) ans = ans * base % mod;
        base = base * base % mod;
        p >>= 1;
    }
    return ans;
}
int n, m, k, ans = 1, chu = 1, cnt;
signed main(){
    scanf("%lld%lld%lld", &n, &m, &k);
    for(register int i = n * m - 2; i >= n * m - k + 1; --i) ans = ans * i % mod;
    for(register int i = k - 2; i >= 1; --i) chu = chu * i % mod;
    ans = (ans * fpow(chu, mod - 2)) % mod;
    for(register int d = 1; d < n; ++d){
    	int x = (n - d) * m, y = m;
    	cnt = (cnt + (x * y % mod) * d % mod) % mod;
	}
	for(register int d = 1; d < m; ++d){
		int x = (m - d) * n, y = n;
		cnt = (cnt + (x * y % mod) * d % mod) % mod;
	}
    printf("%lld\n", ans * cnt % mod);
    return 0;
}