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 unsigned long long MOD = 1000000007;
unsigned long long dp[1005][30];
int main() {
  int N, M;
  cin >> N >> M;
  for (int i = 1; i <= N; i++) dp[i][1] = 1;
  for (int m = 2; m <= 2 * M; m++) {
    for (int n = 1; n <= N; n++) {
      for (int i = n; i <= N; i++) {
        dp[n][m] += dp[i][m - 1] % MOD;
      }
    }
  }
  unsigned long long ans = 0;
  for (int i = 1; i <= N; i++) {
    ans += dp[i][2 * M];
    ans %= MOD;
  }
  cout << ans;
}
