B"In this task Anna and Maria play the following game. Initially they have a checkered piece of paper with a painted n xe2 x80 x89 xc3 x97 xe2 x80 x89m 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, xe2 x80 x89m, xe2 x80 x89k (1 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89n, xe2 x80 x89m, xe2 x80 x89k xe2 x80 x89 xe2 x89 xa4 xe2 x80 x891000). 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 xe2 x80 x89+ xe2 x80 x897). 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 xe2 x80 x89 xc3 x97 xe2 x80 x891 square inside the given 3 xe2 x80 x89 xc3 x97 xe2 x80 x893 square. In the second sample Anna has as much as 9 variants: 4 ways to paint a 1 xe2 x80 x89 xc3 x97 xe2 x80 x891 square, 2 ways to insert a 1 xe2 x80 x89 xc3 x97 xe2 x80 x892 rectangle vertically, 2 more ways to insert it horizontally and one more way is to insert a 2 xe2 x80 x89 xc3 x97 xe2 x80 x892 square."...