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]. 
M=1000000007
n,m=map(int,input().split())
arr=[[1]*n for x in range(m)]
for x in range(1,m):
	for y in range(1,n):
		arr[x][y]=(arr[x-1][y]+arr[x][y-1])%M
cumsum=[arr[m-1][0] for x in range(n)]
for x in range(1,n):
	cumsum[x]=(cumsum[x-1]+arr[m-1][x])%M
ans=0
i=0
j=n-1
while i<n: 
	ans+=(((arr[m-1][j]*cumsum[i])%M)%M)
	j-=1
	i+=1
print(ans%M)