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 n, m;
long long int dp[22][1002];
long long int solve(long long int pos, long long int lastused) {
  if (dp[pos][lastused] != -1) return dp[pos][lastused];
  if (pos > 2 * m) return 1;
  long long int ans = 0, nextuse;
  for (nextuse = lastused; nextuse < n + 1; nextuse++) {
    ans += solve(pos + 1, nextuse);
    ans = ans % 1000000007;
  }
  return dp[pos][lastused] = ans;
}
int main() {
  scanf("%lld %lld", &n, &m);
  memset(dp, -1, sizeof(dp));
  cout << solve(1, 1) << endl;
  return 0;
}
