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
# -*- coding utf-8 -*-
import math


def calc_C(n, r):
    return (math.factorial(n) // (math.factorial(n - r) * math.factorial(r))) % (10**9 + 7)


N, M, K = map(int, input().split())

ans = 0

# row
for i in range(N):
    ans += i * (N - i) * M * M % (10**9 + 7)

# col
for i in range(M):
    ans += i * (M - i) * N * N % (10**9 + 7)

ans = ans % (10**9 + 7)
ans = ans * calc_C(N * M - 2, K - 2) % (10**9 + 7)
print(ans)
