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;
long long dp[15][1005], t[15][1005];
const int MOD = 1e9 + 7;
int main() {
  int n, m;
  cin >> n >> m;
  for (int i = 1; i <= m; ++i) {
    for (int j = 1; j <= n; ++j) {
      dp[1][j] = 1;
      for (int k = 1; k <= j; ++k)
        dp[i][j] = (dp[i - 1][k] + dp[i][j]) % MOD,
        t[i][j] = (t[i][j - 1] + dp[i][j]) % MOD;
    }
  }
  long long res = 0;
  for (int i = 1; i <= n; ++i) {
    long long rs = t[m][n - i + 1] - t[m][0];
    dp[m][i] = dp[m][i] % MOD * rs % MOD;
    res = (res + dp[m][i]) % MOD;
  }
  cout << res;
  return 0;
}
