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]. 
MODULO = 10**9+7
MAX_N = 1000+100

facts = [1 for _ in range(MAX_N)]
for i in range(1, MAX_N):
	facts[i] = (i*facts[i-1]) % MODULO

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

m_1_fact_1 = pow(facts[m-1], MODULO-2, MODULO)

def get_combinations(variants, m):
	line = variants + m - 2
	i = m - 1

	ans = 1
	for j in range(i):
		ans *= line - j
		ans %= MODULO

	# if facts[line] // facts[i] // facts[line-i] != 0:
	# print("variants: {}, m: {}, get_combinations: {}".format(variants, m, facts[line] / facts[i] / facts[line-i]))
	return (ans * m_1_fact_1) % MODULO
	# (facts[line] * pow(facts[i], MODULO-2, MODULO) * pow(facts[line-i], MODULO-2, MODULO)) % MODULO



ans = 0 
for a_border in range(1, n+1):
	for b_border in range(a_border, n+1):
		# print("a_border: {}, b_border: {}".format(a_border, b_border))
		ans += get_combinations(a_border, m) * get_combinations(n - b_border+1, m)
		ans = ans % MODULO
		# print("ans: {}".format(ans))

print(ans)