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 MOD = 1e9 + 7;
const int N = 1e3 + 10;
long long dp1[15][N], dp2[15][N];
int main() {
  int n, m;
  cin >> n >> m;
  for (int i = 1; i <= n; i++) dp1[1][i] = dp2[1][i] = 1;
  for (int i = 2; i <= m; i++)
    for (int j = 1; j <= n; j++)
      for (int k = 1; k <= j; k++) dp1[i][j] += dp1[i - 1][k], dp1[i][j] %= MOD;
  for (int i = 2; i <= m; i++)
    for (int j = 1; j <= n; j++)
      for (int k = j; k <= n; k++) dp2[i][j] += dp2[i - 1][k], dp2[i][j] %= MOD;
  long long ans = 0;
  for (int i = 1; i <= n; i++)
    for (int j = i; j <= n; j++) ans += dp1[m][i] * dp2[m][j], ans %= MOD;
  cout << ans << '\n';
  return 0;
}
