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.

Input

The first and only line contains three integers: $*n*, *m*, *k*$ ($1 ≤ *n*, *m*, *k* ≤ 1000$).

Output

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

Note

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 $1 × 1$ square inside the given $3 × 3$ square.

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