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())
MOD = 10**9 + 7


current_array = [[0 for i in range(n + 1)] for i in range(n + 1)]
prefix_current_array = [[0 for i in range(n + 1)] for i in range(n + 1)]
for i in range(1, m + 1):
	if i == 1:
		for x in range(1, n + 1):
			for y in range(x, n + 1):
				current_array[x][y] = 1
	else:
		next_array = [[0 for i in range(n + 1)] for i in range(n + 1)]
		for x in range(1 , n + 1):
			for y in range(x, n + 1):
				next_array[x][y] = (prefix_current_array[n][y] -
					prefix_current_array[x - 1][y]) % MOD
		current_array = next_array
	for x in range(1, n + 1):
		current_y_sum = 0
		for y in range(1, n + 1):
			current_y_sum = (current_y_sum + current_array[x][y]) % MOD
			prefix_current_array[x][y] = (current_y_sum +
				prefix_current_array[x - 1][y]) % MOD
	#print("i =", i)
	#print(current_array)
	#print(prefix_current_array)

print(prefix_current_array[n][n])



