Problem Statement

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 $10^9+7$.