Problem Statement

There is a rectangular sheet of paper with height H+1 and width W+1. We introduce an xy-coordinate system so that the four corners of the sheet are (0, 0), (W + 1, 0), (0, H + 1) and (W + 1, H + 1).
This sheet can be cut along the lines x = 1,2,...,W and the lines y = 1,2,...,H. Consider a sequence of operations of length K where we choose K of these H + W lines and cut the sheet along those lines one by one in some order.
Let the score of a cut be the number of pieces of paper that exist just after the cut. The score of a sequence of operations is the sum of the scores of all of the K cuts.
Find the sum of the scores of all possible sequences of operations of length K. Since this value can be extremely large, print the number modulo 10^9 + 7.

Input

Input is given from Standard Input in the following format:
H W K

Output

Print the sum of the scores, modulo 10^9 + 7.

Constraints

• $1 \leq H,W \leq 10^7$
• $1 \leq K \leq H + W$
• H, W and K are integers.

Sample Input 1

2 1 2

Sample Output 1

34

Let x_1, y_1 and y_2 denote the cuts along the lines x = 1, y = 1 and y = 2, respectively. The six possible sequences of operations and the score of each of them are as follows:

• y_1, y_2: 2 + 3 = 5
• y_2, y_1: 2 + 3 = 5
• y_1, x_1: 2 + 4 = 6
• y_2, x_1: 2 + 4 = 6
• x_1, y_1: 2 + 4 = 6
• x_1, y_2: 2 + 4 = 6

The sum of these is 34.

Sample Input 2

30 40 50

Sample Output 2

616365902

Be sure to print the sum modulo 10^9 + 7.

见题面 Input 部分

见题面 Output 部分