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:
#!/usr/bin/env python3
import atexit
import io
import sys

_I_B = sys.stdin.read().splitlines()
input = iter(_I_B).__next__
_O_B = io.StringIO()
sys.stdout = _O_B

@atexit.register
def write():
	sys.__stdout__.write(_O_B.getvalue())


def main():
	u,v=map(int,input().split())
	if u>v:
		print(-1)
	elif u==v:
		if u:
			print(1,u,sep="\n")
		else:
			print(u)
	else:
		if (v-u)&1:
			print(-1)
		else:
			v2=(v-u)//2
			if u+v2 == u^(v2):
				print(2)
				print(v2,u+v2)
			else:
				print(3)
				print(u,v2,v2)

if __name__=='__main__':
	main()