Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

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

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jan/29/2020 12:48:53 (e1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|