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())
#a rosnie, b maleje, a mniejsza od b 
#a_ost <= b_pier
m *= 2
odp = 1
p = 10**9 + 7
c = 1001
#multipodzbiorów m eltowych zbioru n eltowego dp[m][n]
dp = [[0 for i in range(c)] for j in range(21)]
for i in range(21):
	dp[i][1] = 1
for j in range(c):
	dp[1][j] = j
for i in range(2,21):
	for j in range(2,c):
		dp[i][j] = (dp[i-1][j] +dp[i][j-1])%p
#for i in range(c):
#	print(dp[i])
print(dp[m][n])