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;
using python = void;
long long cs[1111][1111];
signed main() {
  cin.tie(0);
  cout.tie(0);
  ios_base::sync_with_stdio(0);
  ;
  long long n, m;
  cin >> n >> m;
  if (n == 1) {
    cout << 1 << '\n';
    return 0;
  }
  cs[0][1] = 1;
  for (long long i = 1; i <= m + 1; i++) {
    for (long long j = 1; j <= n; j++)
      cs[i][j] = (cs[i - 1][j] + cs[i][j - 1]) % 1000000007;
  }
  long long res = 0;
  for (long long i = 0; i < n; i++) {
    for (long long j = i; j < n; j++) {
      long long is = i + 1, js = n - j;
      res = (res + ((cs[m][js] * cs[m][is]) % 1000000007)) % 1000000007;
    }
  }
  cout << res << '\n';
}
