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 Problem1325d {
    public static void main(String args[]) {
        Scanner input=new Scanner(System.in);
        long u = input.nextLong();
        long v = input.nextLong();
        if(u>v || (v-u)%2 == 1) {
            System.out.println(-1);
        }
        else if(u==v) {
            if(u==0) {
                System.out.println(0);
            }
            else {
                System.out.println(1);
                System.out.println(v);
            }
        }
        else {
            long x=u;
            long y=(v-u)/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);
            }
        }
    }
}