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 (109 + 7).

Examples

Input

1 1


Output

0


Input

4 4


Output

485


Input

3 5


Output

451
#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;
#define int long long
const int N=2010,p=1000000007;
int n,m,f[N][N],ans,s;
main(){
	scanf("%lld%lld",&n,&m);
	for (int i=1;s=0,i<=n;++i)
		for (int j=0;j<=m-2;++j)
		s=(s+f[i-1][j])%p,f[i][j]=((j==0?1:f[i][j-1])+s)%p;
	for (int i=1;i<=n;++i)
		for (int j=0;j<=m-2;++j)
		ans=(ans+(m-j-1)*(f[i][j]-f[i-1][j])%p*f[n-i+1][j]%p)%p;
	printf("%lld",ans);
	return 0;
}

/*
题目大意：
		在一个n*m的棋盘中，求存在如下图形时的方案数。
	_________
	____**___
	__*___*__
	__*___*__ 
	__*__*___
	___**____ 
	_________
	_________ 
		
解法：
*/
   			 		 	  		  					 	 		  		