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 MAXN = 1E3 + 2;
const long long MAXM = 22;
const long long MOD = 1E9 + 7;
long long n, m;
long long f[MAXM][MAXN];
long long dp(long long i, long long mx) {
  long long& ret = f[i][mx];
  if (ret != -1) return ret;
  if (i == 2 * m + 1) return ret = 1;
  ret = 0LL;
  for (long long j = max(1LL, mx); j <= n; ++j) {
    ret += dp(i + 1, j);
    ret %= MOD;
  }
  return ret;
}
signed main() {
  cin >> n >> m;
  memset(f, -1, sizeof f);
  cout << dp(1, 0) << "\n";
}
