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 t, k, n, m, a, b, total, count1, count2, hell = 1000000007;
;
long long modInverse(long long x, unsigned int y, unsigned int m) {
  if (y == 0) return 1;
  long long p = modInverse(x, y / 2, m) % m;
  p = (p * p) % m;
  return (y % 2 == 0) ? p : (x * p) % m;
}
long long nCr(long long n, long long r, long long m) {
  long long ans = 1;
  for (long long i = r + 1; i <= n; i++) ans = ((ans % m) * (i % m) % m);
  for (int i = 2; i <= (n - r); i++) {
    ans = ((ans % m) * (modInverse(i, m - 2, m))) % m;
  }
  return ans;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  srand(chrono::high_resolution_clock::now().time_since_epoch().count());
  cin >> n >> m;
  m = 2 * m;
  if (n >= m) {
    for (int i = 1; i <= m; i++) {
      total = ((total % hell) +
               (nCr(n, i, hell) % hell) * ((nCr(m - 1, i - 1, hell)) % hell)) %
              hell;
    }
  } else {
    for (int i = 1; i <= n; i++) {
      total = ((total % hell) +
               (nCr(n, i, hell) % hell) * ((nCr(m - 1, i - 1, hell)) % hell)) %
              hell;
    }
  }
  cout << total;
  return 0;
}
