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;
const int maxn = 1e5 + 10;
int n, m;
long long dp[25][1005];
int main() {
  scanf("%d%d", &n, &m);
  m <<= 1;
  for (int i = 0; i <= n; i++) {
    dp[0][i] = 1;
  }
  for (int i = 1; i <= m; i++) {
    for (int j = 1; j <= n; j++) {
      dp[i][j] = (dp[i - 1][j] + dp[i][j - 1]);
      dp[i][j] %= 1000000007;
    }
  }
  printf("%lld\n", dp[m][n]);
  return 0;
}
