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 <bits/stdc++.h>
using namespace std;
const int maxn = 2000 + 7;
const int mod = 1000000000 + 7;
int n, m, f[maxn][maxn], g[maxn][maxn];
int s[maxn][maxn];
void prework() {
  memset(f, 0, sizeof(f));
  memset(g, 0, sizeof(g));
  for (int k = 1; k <= n; k++) {
    int sum = 0, w = 0, sumg = 0;
    for (int i = 2; i <= m; i++) {
      w = (w + f[k - 1][i]) % mod;
      sum = (sum + w) % mod;
      f[k][i] = (sum + 1) % mod;
      sumg = (f[k][i] + sumg) % mod;
      g[k][i] = (g[k][i - 1] + sumg) % mod;
    }
  }
}
int main() {
  scanf("%d%d", &n, &m);
  prework();
  long long ans = 0;
  for (int i = 1; i <= n; i++) {
    for (int j = 2; j <= m; j++) {
      ans = (ans + (long long)(f[i][j]) * (g[n - i][j] - f[n - i][j] + 1) %
                       mod * (m - j + 1) % mod) %
            mod;
    }
  }
  printf("%I64d\n", ans);
  return 0;
}
