A9061 | Greg and Caves

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 $[l,r]$ $(1<=l<=r<=n)$ , 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.

The first line contains two integers $n$ , $m$ — the pad's screen size $(1<=n,m<=2000)$ .

In the single line print the remainder after dividing the answer to the problem by $1000000007$ $(10^{9}+7)$ .