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 int mod = 1000000007;
long long n, m;
long long dp[1010][22];
long long rec(long long pos, long long val) {
  if (pos >= 2 * m) {
    return 1;
  }
  long long &ans = dp[val][pos];
  if (ans != -1) return ans;
  ans = rec(pos + 1, val);
  for (long long i = val + 1; i < n + 1; i++) {
    ans = (ans + rec(pos + 1, i)) % mod;
  }
  return ans % mod;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  cin >> n >> m;
  memset(dp, -1, sizeof dp);
  cout << rec(0, 1);
  return 0;
}
