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 maxn = 1022, mod = 1e9 + 7;
int fac[maxn], inv[maxn];
int mod_exp(int n, int p) {
  if (p == -1) p = mod - 2;
  int ret = 1;
  while (p) {
    if (p & 1) ret = (ret * 1LL * n) % mod;
    p >>= 1;
    n = (n * 1LL * n) % mod;
  }
  return ret;
}
void init() {
  fac[0] = 1;
  for (int i = 1; i < maxn; i++) fac[i] = (fac[i - 1] * 1LL * i) % mod;
  inv[maxn - 1] = mod_exp(fac[maxn - 1], -1);
  for (int i = maxn - 2; i >= 0; i--)
    inv[i] = (inv[i + 1] * 1LL * (i + 1)) % mod;
}
int nCr(int n, int r) {
  return ((fac[n] * 1LL * inv[r]) % mod) * inv[n - r] % mod;
}
int main() {
  int n, m;
  init();
  cin >> n >> m;
  cout << nCr(n + 2 * m - 1, 2 * m);
  return 0;
}
