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]. 
mod = int(1e9 + 7)

n, m = map(int, input().split())

def fact(n):
	ans = 1
	for i in range(2, n+1):
		ans = (ans * i) % mod
	return ans

def modinv(a, m):
	def egcd(a, b):
		if a == 0:
			return (b, 0, 1)
		g, y, x = egcd(b % a, a)
		return (g, x - (b // a) * y, y)
	g, x, y = egcd(a, m)
	return x % m

num = fact(n + 2*m - 1)
den = (fact(2*m) * fact(n - 1) ) % mod
print((num * modinv(den, mod)) % mod)