In this task Anna and Maria play the following game. Initially they have a checkered piece of paper with a painted n \times m rectangle (only the border, no filling). Anna and Maria move in turns and Anna starts. During each move one should paint inside the last-painted rectangle a new lesser rectangle (along the grid lines). The new rectangle should have no common points with the previous one. Note that when we paint a rectangle, we always paint only the border, the rectangles aren't filled.

Nobody wins the game - Anna and Maria simply play until they have done k moves in total. Count the number of different ways to play this game.

The first and only line contains three integers: n,m,k (1 \le n,m,k \le 1000).

Print the single number - the number of the ways to play the game. As this number can be very big, print the value modulo 1000000007 (109+7).

Two ways to play the game are considered different if the final pictures are different. In other words, if one way contains a rectangle that is not contained in the other way.

In the first sample Anna, who performs her first and only move, has only one possible action plan - insert a 1 \times 1 square inside the given 3 \times 3 square.

In the second sample Anna has as much as 9 variants: 4 ways to paint a 1 \times 1 square, 2 ways to insert a 1 \times 2 rectangle vertically, 2 more ways to insert it horizontally and one more way is to insert a 2 \times 2 square.