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 int pow1(long long int a, long long int b) {
  long long int ans = 1;
  while (b) {
    if (b & 1) {
      ans = ans * a;
    }
    a = a * a;
    b = b >> 1;
  }
  return ans;
}
long long int mod = 1000000007;
long long int nCr(long long int n, long long int r) {
  long long int c[r + 1];
  memset(c, 0, sizeof(c));
  c[0] = 1;
  long long int i, j;
  for (i = 1; i <= n; i++)
    for (j = min(n, r); j > 0; j--) c[j] = (c[j] + c[j - 1]) % mod;
  return c[r];
}
int main() {
  long long int n, m, i, j;
  cin >> n >> m;
  cout << nCr((2 * m) + (n - 1), (2 * m)) << endl;
  return 0;
}
