D. Petya and Coloringtime limit per test5 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputLittle Petya loves counting. He wants to count the number of ways to paint a rectangular checkered board of size n × 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.InputThe first line contains space-separated integers n, m and k (1 ≤ n, m ≤ 1000, 1 ≤ k ≤ 106) — the board's vertical and horizontal sizes and the number of colors respectively.OutputPrint the answer to the problem. As the answer can be quite a large number, you should print it modulo 109 + 7 (1000000007).ExamplesInput2 2 1Output1Input2 2 2Output8Input3 2 2Output40
Input2 2 1
Output1
['combinatorics', 'dp', '*2300']