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 M = 1e9 + 7;
int n, m;
long long iv[1000];
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cin >> n >> m;
  iv[1] = 1;
  for (int i = 2; i < 1000; ++i) iv[i] = M - M / i * iv[M % i] % M;
  long long ans = 1;
  for (int i = 1; i <= n + 2 * m - 1; ++i) ans = ans * i % M;
  for (int i = 1; i <= 2 * m; ++i) ans = ans * iv[i] % M;
  for (int i = 1; i <= n - 1; ++i) ans = ans * iv[i] % M;
  cout << ans;
}
