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.

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 $1000000007$ $(10^{9} + 7)$.