Little Petya loves counting. He wants to count the number of ways to paint a rectangular checkered board of size n \times m (n rows, m columns) in k colors. Besides, the coloring should have the following property: for any vertical line that passes along the grid lines and divides the board in two non-empty parts the number of distinct colors in both these parts should be the same. Help Petya to count these colorings.

The first line contains space-separated integers n, m and k (1 \le n,m \le 1000,1 \le k \le 106) - the board's vertical and horizontal sizes and the number of colors respectively.

Print the answer to the problem. As the answer can be quite a large number, you should print it modulo 109+7 (1000000007).