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.Scanner;

public class Xorcist{
    public static void main(String[] args){
        Scanner obj=new Scanner(System.in);
        long u=obj.nextLong();
        long v=obj.nextLong();
        if(u>v){
            System.out.println("-1");
        }else if(u==0&&v==0){
            System.out.println(0);
        }
        else if(u==v){
            System.out.println(1);
            System.out.println(u);
        }else if((u+v)%2!=0){
            System.out.println("-1");
        }
        else{
            long x=(v-u)/2;
            if((x&u)==0){
                System.out.println(2);
                System.out.println((u+x)+" "+x);
            }else{
                System.out.println(3);
                System.out.println(u+" "+x+" "+x);
            }
        }
    }
}