Problem3248--Greg and Caves

3248: Greg and Caves

Time Limit: 2 Sec  Memory Limit: 256 MB
Submit: 0  Solved: 0
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Description

time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Greg has a pad. The pad's screen is an n×m rectangle, each cell can be either black or white. We'll consider the pad rows to be numbered with integers from 1 to n from top to bottom. Similarly, the pad's columns are numbered with integers from 1 to m from left to right.

Greg thinks that the pad's screen displays a cave if the following conditions hold:

  • There is a segment [l,r] (1≤lrn), such that each of the rows l,l+1,...,r has exactly two black cells and all other rows have only white cells.
  • There is a row number t (ltr), such that for all pairs of rows with numbers i and j (lijt) the set of columns between the black cells in row i (with the columns where is these black cells) is the subset of the set of columns between the black cells in row j (with the columns where is these black cells). Similarly, for all pairs of rows with numbers i and j (tijr) the set of columns between the black cells in row j (with the columns where is these black cells) is the subset of the set of columns between the black cells in row i (with the columns where is these black cells).

Greg wondered, how many ways there are to paint a cave on his pad. Two ways can be considered distinct if there is a cell that has distinct colors on the two pictures.

Help Greg.

Input

The first line contains two integers n, m − the pad's screen size (1≤n,m≤2000).

Output

In the single line print the remainder after dividing the answer to the problem by 1000000007 (109+7).

Examples
Input
1 1
Output
0
Input
4 4
Output
485
Input
3 5
Output
451

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