# #P295D. Greg and Caves

ID: 5762 Type: RemoteJudge 2000ms 256MiB 尝试: 1 已通过: 1 难度: 9 上传者: 标签>combinatoricsdp*2400

# Greg and Caves

## Description

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 (109 + 7).

## 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).

## Samples

``````1 1

``````
``````0

``````
``````4 4

``````
``````485

``````
``````3 5

``````
``````451

``````