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]. 
def prodTree(l, r):
    if l > r:
        return 1
    if l == r:
        return l
    if r - l == 1:
        return l * r
    m = int((l + r) // 2)

    return prodTree(l, m) * prodTree(m + 1, r)

def factorial(n):
    if n < 0:
        return False
    if n == 0:
        return 1
    if n == 1 and n == 2:
        return n
    return prodTree(2, n)


n, m = [int(i) for i in input().split()]

print((factorial(n + 2 * m - 1) // (factorial(2*m) * factorial(n - 1))) % int(1e9 + 7))