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 sun.reflect.generics.tree.Tree;

import java.lang.reflect.Array;
import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        long n = sc.nextLong();
        long m = sc.nextLong();

        if(n>m)
            System.out.println(-1);
        else if(n==0&&m==0)
            System.out.println(0);
        else if(n==m)
            System.out.println(1+"\n"+m);
        else if((m-n)%2==0)
        {
            long x=n;long y=(m-n)/2;
            long z=x^y;
            if(z+y==m){
                System.out.println(2);
                System.out.println(z+" "+y);
            }else{
                System.out.println(3);
                System.out.println(x+" "+y+" "+y);
            }
        }else
            System.out.println(-1);
    }

}