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]. 
n,m=map(int, input().split())
b=[(1) for i in range(n)]
a=[(1) for i in range(n)]
s=n
for i in range(m-1):
    nes=0
    news=0
    for j in range(n):
        nes=nes+b[j]
        b[j]=b[j]+s-nes
        news=news+b[j]
        a[n-j-1]=b[j]
    s=news
s=0
for i in range(n):
    s1=0
    for j in range(i+1):
        s1=s1+a[j]
    s=s+s1*b[i]
print(s%(10**9+7))
