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 PYTHON):

Solution:
import sys
u,v = map(int,raw_input().split())
if u > v:
	print -1
	sys.exit()
elif u == v:
	if u == 0:
		print 0
	else:
		print 1
		print u
	sys.exit()
diff = v-u
if diff%2==0:
	if u:
		if (diff/2)^u == (diff/2)+u:
			print 2
			print diff/2,(diff/2)^u
		else:
			print 3
			print diff/2,diff/2,u
	else:
		print 2
		print diff/2,diff/2
	sys.exit()
print -1