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 JAVA):

Solution:
import java.util.*;
public class Main { 
 public static void main(String args[])
 {
	 Scanner input=new Scanner(System.in);
	 long or=input.nextLong();long sum=input.nextLong();
	 if(or>sum||(sum-or)%2==1)
		 System.out.println(-1);
	 else if(or==sum)
	 {
		 if(or==0)System.out.println(0);
		 else
		 {
		 System.out.println(1);
		 System.out.println(sum);}
	 }
	 else
	 {
		long x=or;long y=(sum-or)/2;
		if((x&y)==0)
		{
			System.out.println(2);
			System.out.print(x+y+" "+y);
		}
		else
		{
			System.out.println(3);
			System.out.println(x+" "+y+" "+y);
		}
	 }
 }
}