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(' '))
# the number filled(1-n)  , number of ways of i length array
dp=[[0]*(n+1) for _ in range(2*m+1)]

dp[1] = [0]+[1]*n

mm = 1000000007

for j in range(2,2*m+1):
	dp[j] = [a%mm for a in dp[j-1]]

	for i in range(n-1, 0,-1):

		dp[j][i] = (dp[j][i+1]%mm + dp[j-1][i]%mm )%mm


#print(dp)
print(sum(dp[2*m])%mm)



