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 long long mod = 1e9 + 7;
long long q[1007][15];
int main() {
  int n, m;
  long long an = 0;
  cin >> n >> m;
  for (int i = 0; i < 15; i++) q[1][i] = 1;
  for (int i = 0; i < 1005; i++) q[i][0] = 1;
  for (int x = 2; x <= 1005; x++)
    for (int y = 1; y <= 10; y++) {
      q[x][y] = (q[x - 1][y] + q[x][y - 1]) % mod;
    }
  for (int i = 1; i <= n; i++) an += (q[i][m - 1] * q[n - i + 1][m]) % mod;
  cout << an % mod << endl;
  return 0;
}
