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D. Petya and Coloring

time limit per test

5 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard 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.

Input

The first line contains space-separated integers *n*, *m* and *k* (1 ≤ *n*, *m* ≤ 1000, 1 ≤ *k* ≤ 10^{6}) — the board's vertical and horizontal sizes and the number of colors respectively.

Output

Print the answer to the problem. As the answer can be quite a large number, you should print it modulo 10^{9} + 7 (1000000007).

Examples

Input

2 2 1

Output

1

Input

2 2 2

Output

8

Input

3 2 2

Output

40

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