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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class Main {


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

        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String[] s = br.readLine().trim().split(" ");
        long u = Long.parseLong(s[0]);
        long v = Long.parseLong(s[1]);
        if(u>v || u%2!=v%2){
            System.out.println(-1);
            System.exit(0);
        }
        if(u==v){
            if(u==0){
                System.out.println(0);
            }else {
                System.out.println(1);
                System.out.println(u);
            }

            System.exit(0);
        }
        long x = (v-u)/2;
        long p = u&x;
        if(p!=0){
            System.out.println(3);
            System.out.println(u+" "+x+" "+x);
        }else {
            System.out.println(2);
            System.out.println(String.valueOf(u^x)+" "+x);
        }


    }


}