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 Comb[2004][1004];
long long C(long long n, long long r) {
  if (Comb[n][r]) return Comb[n][r];
  if (n == r || r == 0) return 1;
  return Comb[n][r] = (C(n - 1, r - 1) + C(n - 1, r)) % MOD;
}
long long H(long long n, long long m) { return C(n + m - 1, m) % MOD; }
int main() {
  long long n, m;
  scanf("%lld%lld", &n, &m);
  long long ans = H(n, 2 * m) % MOD;
  printf("%lld\n", ans);
  return 0;
}
