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 Ja{

 	 public static void main(String args[] ) throws Exception {

 	 	Scanner s=new Scanner(System.in);
 	 	long u=s.nextLong();
 	 	long v=s.nextLong();
 	 	//int min=1000000,small=0,large=0;
 	     if (u%2!=v%2 || u>v)
    {
        System.out.println("-1");
       
    }
    else if (u==v)
    {
        if (u==0)
       System.out.println("0");
        else{
        System.out.println("1");
        System.out.println(u);
    }
    }
    else{
    long x=(v-u)/2;
    if (!((u^x)==u+x)){
    System.out.println("3");
    System.out.print(u+" "+x+" "+x);
    }else{
    System.out.println("2");
    System.out.println((u^x)+" "+x);
    }
        
    }
 	 }
 }