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

#sys.stdin = open('problem_a.txt', 'r')
raw_input = sys.stdin.readline

int_input = lambda : int(raw_input())
format_input = lambda type: map(type, raw_input().split())
list_input = lambda: list(raw_input().strip())
format_list = lambda type, list: map(type, list)


u, v = format_input(int)
if u > v or u%2 != v%2:
	print -1
else:
	if u == v == 0:
		print 0
	elif u == v:
		print 1
		print u
	else:
		tmp1 = (v - u) / 2
		tmp2 = v - tmp1
		if tmp1 ^ tmp2 != u:
			print 3
			print tmp1, tmp1, v - 2 * tmp1 
		else:
			print 2
			print tmp1 , tmp2