A8318 | Games with Rectangle

In this task Anna and Maria play the following game. Initially they have a checkered piece of paper with a painted $n×m$ 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: $n,m,k$ ( $1<=n,m,k<=1000$ ).

Print the single number — the number of the ways to play the game. As this number can be very big, print the value modulo $1000000007$ ( $10^{9}+7$ ).