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;
int f[2100][2100], sum1[2100][2100], sum2[2100][2100];
int main() {
  int n, m, i, j, k, x, y, ans;
  scanf("%d%d", &n, &m);
  f[0][0] = 1;
  f[1][0] = 1;
  for (i = 2; i <= m; i++) f[1][i] = 1;
  for (i = 0; i <= 1; i++) {
    sum1[i][0] = 0;
    sum2[i][0] = 0;
    for (j = 1; j <= m; j++) {
      sum1[i][j] = f[i][j] + sum1[i][j - 1];
      sum2[i][j] = (long long)j * f[i][j] % 1000000007 + sum2[i][j - 1];
      if (sum1[i][j] >= 1000000007) sum1[i][j] -= 1000000007;
      if (sum2[i][j] >= 1000000007) sum2[i][j] -= 1000000007;
    }
  }
  for (i = 2; i <= n; i++) {
    f[i][0] = 1;
    for (j = 2; j <= m; j++) {
      f[i][j] = ((long long)sum1[i - 1][j] * (j + 1) % 1000000007 -
                 sum2[i - 1][j] + 1 + 1000000007) %
                1000000007;
    }
    sum1[i][0] = 0;
    sum2[i][0] = 0;
    for (j = 1; j <= m; j++) {
      sum1[i][j] = f[i][j] + sum1[i][j - 1];
      sum2[i][j] = (long long)j * f[i][j] % 1000000007 + sum2[i][j - 1];
      if (sum1[i][j] >= 1000000007) sum1[i][j] -= 1000000007;
      if (sum2[i][j] >= 1000000007) sum2[i][j] -= 1000000007;
    }
  }
  ans = 0;
  for (i = 1; i <= n; i++) {
    for (j = 2; j <= m; j++) {
      ans += ((long long)sum1[i - 1][j - 1] * (j + 1) % 1000000007 -
              sum2[i - 1][j - 1] + 1000000007 + 1) %
             1000000007 * f[n - i + 1][j] % 1000000007 * (m - j + 1) %
             1000000007;
      if (ans >= 1000000007) ans -= 1000000007;
    }
  }
  printf("%d\n", ans);
  return 0;
}
