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D. Greg and Caves

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputGreg 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 ≤*l*≤*r*≤*n*), 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*(*l*≤*t*≤*r*), such that for all pairs of rows with numbers*i*and*j*(*l*≤*i*≤*j*≤*t*) 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*(*t*≤*i*≤*j*≤*r*) 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 (10^{9} + 7).

Examples

Input

1 1

Output

0

Input

4 4

Output

485

Input

3 5

Output

451

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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