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 C628_PD {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner in = new Scanner(System.in);
		long u = in.nextLong();
		long v = in.nextLong();
		if(u>v||u%2!=v%2)
		{
			System.out.println(-1);
			return;
		}
		if(u==v)
		{
			if(u==0)
				System.out.println(0);
			else
			{
				System.out.println(1);
				System.out.println(u);
			}
			return;
		}
		long x = (v-u)/2;
		if((u&x)!=0)
		{
			System.out.println(3);
			System.out.println(u+ " "+x+" "+x );
		}
		else
		{
			System.out.println(2);
			System.out.println((u^x)+ " "+x );
		}
	}

}