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 int MOD = 1e9 + 7;
long long dp[1001][1001];
long long sdp[1001][1001];
long long ssdp[1001][1001];
long long ssdp2[1001];
int main() {
  std::ios::sync_with_stdio(false);
  cin.tie(0);
  int n, m;
  cin >> n >> m;
  for (int i = 0; i <= n; ++i) {
    for (int j = 0; j <= n; ++j) {
      dp[i][j] = 1;
    }
  }
  for (int u = 1; u <= m; ++u) {
    for (int l = 1; l <= n; ++l) {
      for (int r = 1; r <= n; ++r) {
        sdp[l][r] = (sdp[l][r - 1] + dp[l][r]) % MOD;
      }
    }
    for (int r = 1; r <= n; ++r) {
      for (int l = 1; l <= n; ++l) {
        ssdp[r][l] = (ssdp[r][l - 1] + sdp[l][r]) % MOD;
      }
      ssdp2[r] = (sdp[r][r - 1] + ssdp2[r - 1]) % MOD;
    }
    for (int r = 1; r <= n; ++r) {
      for (int l = 1; l <= r; ++l) {
        dp[l][r] = (ssdp[n][l] - ssdp[r - 1][l]) % MOD;
      }
      for (int l = r + 1; l <= n; ++l) {
        dp[l][r] = (ssdp[n][l] - ssdp[r - 1][r] - ssdp2[l] + ssdp2[r]) % MOD;
      }
    }
  }
  cout << (dp[n][1] + MOD) % MOD;
}
