Problem: Given 2 integers u and v, find the shortest array such that [bitwise-xor](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) of its elements is u, and the sum of its elements is v.

Input

The only line contains 2 integers u and v (0 ≤ u,v ≤ 10^{18}).

Output

If there's no array that satisfies the condition, print "-1". Otherwise:

The first line should contain one integer, n, representing the length of the desired array. The next line should contain n positive integers, the array itself. If there are multiple possible answers, print any.

Examples

Input


2 4


Output


2
3 1

Input


1 3


Output


3
1 1 1

Input


8 5


Output


-1

Input


0 0


Output


0

Note

In the first sample, 3⊕ 1 = 2 and 3 + 1 = 4. There is no valid array of smaller length.

Notice that in the fourth sample the array is empty.

Solution (in PYTHON3):

Solution:
xor, sum = map(int, input().split())
answer = []
if xor > sum or (sum - xor) & 1:
	print(-1)
	exit()
elif xor == sum:
	if xor == 0:
		print(0)
		exit()
	answer.append(xor)
else:
	carry = False
	X, S = xor, sum
	xor, sum = bin(xor)[2:][::-1], bin(sum)[2:][::-1]
	xor = xor + '0' * (len(sum) - len(xor))
	answer = ['', '']
	for index, bit_xor, bit_sum in zip(range(len(xor)), xor, sum):
		if bit_xor == bit_sum == '1' and not carry:
			answer[0] += '1'
			answer[1] += '0'
		elif bit_sum == bit_xor == '0' and not carry:
			if index < len(xor) - 1 and sum[index + 1] != xor[index + 1]:
				carry = True
				answer[0] += '1'
				answer[1] += '1'
			else:
				answer[0] += '0'
				answer[1] += '0'
		elif bit_sum == '1' and bit_xor == '0' and carry:
			if index < len(sum) - 1 and sum[index + 1] != xor[index + 1]:
				answer[0] += '1'
				answer[1] += '1'
			else:
				carry = False
				answer[0] += '0'
				answer[1] += '0'
		elif bit_sum == '0' and bit_xor == '1' and carry:
			answer[0] += '1'
			answer[1] += '0'
		else:
			answer = [X, (S - X) // 2, (S - X) // 2]
			carry = None
			break
	if carry == True:
		answer[0].append('1')		
	if carry != None:
		answer = [int(x[::-1], 2) for x in answer]
print(str(len(answer)) + '\n' + ''.join(str(x) + ' ' for x in answer))