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 main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  ;
  int N, M;
  cin >> N >> M;
  M *= 2;
  vector<int> DP(N, 1);
  int i, j, k;
  for (i = 1; i < M; i++) {
    vector<int> Next(N);
    for (j = 0; j < N; j++) {
      for (k = 0; k <= j; k++) {
        Next[j] = ((Next[j] + DP[k]) % 1000000007);
      }
    }
    DP = Next;
  }
  int Result = 0;
  for (i = 0; i < N; i++) {
    Result = ((Result + DP[i]) % 1000000007);
  }
  cout << Result << endl;
  return 0;
}
