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]. 
MOD = 10**9 + 7

def pow_mod(n, k, mod):
  if k == 0:
    return 1
  if k % 2 == 1:
    return (n * pow_mod(n, k-1, mod)) % mod
  else:
    r = pow_mod(n, k // 2, mod)
    return (r * r) % mod

def mod_inverse(n, mod):
  return pow_mod(n, mod - 2, mod)

def fact_mod(n, mod):
  res = 1
  for i in range(2, n+1):
    res = (res * i) % mod
  return res

def choose_mod(n, k, mod):
  return (fact_mod(n, mod) * mod_inverse(fact_mod(k, mod), mod) * mod_inverse(fact_mod(n - k, mod), mod)) % mod 

n, m = map(int, input().split())

print(choose_mod(n + 2*m - 1, 2*m, MOD))