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 std::cin;
using std::cout;
using std::endl;
using std::vector;
long long way(int len, int num) {
  vector<vector<long long>> map(len, vector<long long>(num, 0));
  for (int len_index = 0; len_index < len; ++len_index) {
    for (int num_index = 0; num_index < num; ++num_index) {
      if (len_index == 0)
        map[len_index][num_index] = 1;
      else if (num_index == 0)
        map[len_index][num_index] = len_index + 1;
      else {
        long long map_item =
            map[len_index - 1][num_index] + map[len_index][num_index - 1];
        if (map_item >= (long long)(1e9 + 9)) {
          map_item = map_item % (long long)(1e9 + 7);
        }
        map_item %= (long long)(10e9) + 7;
        map[len_index][num_index] = map_item;
      }
    }
  }
  return map[len - 1][num - 1];
}
int main() {
  int n, m;
  cin >> n >> m;
  cout << way(n, 2 * m);
  return 0;
}
