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 int MOD = 1e9 + 7;
long long int gcd(long long int a, long long int b) {
  if (a == 0) return b;
  return gcd(b % a, a);
}
int32_t main() {
  ios_base::sync_with_stdio(NULL);
  cin.tie(0);
  cout.tie(0);
  long long int n, m, x, temp = 0, fact = 1, i, j;
  cin >> n >> m;
  vector<long long int> a, b;
  x = n + 2 * m - 1;
  for (i = n; i <= x; i++) a.push_back(i);
  for (i = 1; i <= 2 * m; i++) b.push_back(i);
  for (i = 0; i < a.size(); i++) {
    for (j = 0; j < b.size(); j++) {
      temp = gcd(a[i], b[j]);
      a[i] = a[i] / temp;
      b[j] = b[j] / temp;
    }
  }
  for (auto x : a) {
    fact *= x;
    fact %= MOD;
  }
  cout << fact;
  return 0;
}
