You are given two integers n and m. Calculate the number of pairs of arrays (a, b) such that:

  * the length of both arrays is equal to m; 
  * each element of each array is an integer between 1 and n (inclusive); 
  * a_i ≤ b_i for any index i from 1 to m; 
  * array a is sorted in non-descending order; 
  * array b is sorted in non-ascending order. 



As the result can be very large, you should print it modulo 10^9+7.

Input

The only line contains two integers n and m (1 ≤ n ≤ 1000, 1 ≤ m ≤ 10).

Output

Print one integer – the number of arrays a and b satisfying the conditions described above modulo 10^9+7.

Examples

Input


2 2


Output


5


Input


10 1


Output


55


Input


723 9


Output


157557417

Note

In the first test there are 5 suitable arrays: 

  * a = [1, 1], b = [2, 2]; 
  * a = [1, 2], b = [2, 2]; 
  * a = [2, 2], b = [2, 2]; 
  * a = [1, 1], b = [2, 1]; 
  * a = [1, 1], b = [1, 1]. 
#include <bits/stdc++.h>
using namespace std;
int n, m, dp[15 << 1][1005], s[15 << 1][1005];
int main() {
  scanf("%d %d", &n, &m);
  for (int i = 1; i <= n; ++i) s[0][i] = 1;
  for (int i = 1; i <= m << 1; ++i)
    for (int j = 1; j <= n; ++j) {
      dp[i][j] = (dp[i][j] + s[i - 1][j]) % 1000000007;
      s[i][j] = (s[i][j - 1] + dp[i][j]) % 1000000007;
    }
  printf("%d\n", s[m << 1][n]);
  return 0;
}
