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 N = 1100;
const long long MOD = (1e9) + 7;
long long n, m, ans, mem[N][20];
long long dp(long long i, long long j) {
  if (i == 0 && j == 0) return 1;
  if (i == 0 || j == 0) return 0;
  if (mem[i][j] != -1) return mem[i][j];
  long long p = 0;
  for (int k = i; k >= 0; k--) {
    p += dp(k, j - 1);
    p %= MOD;
  }
  return mem[i][j] = p;
}
int main() {
  cin >> n >> m;
  memset(mem, -1, sizeof mem);
  for (int i = n; i >= 1; i--) {
    ans += dp(i, m * 2);
    ans %= MOD;
  }
  cout << ans << endl;
}
