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.*;
import java.util.HashSet;
import java.util.StringTokenizer;
import java.util.ArrayList;

public class EhabtheXocist{


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

        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter writer = new BufferedWriter(new OutputStreamWriter(System.out));
        StringTokenizer tokenizer; 


        tokenizer = new StringTokenizer(reader.readLine());
        long u = Long.parseLong(tokenizer.nextToken());
        long v = Long.parseLong(tokenizer.nextToken());

        if(u%2 != v%2){
            writer.write(String.valueOf(-1));
            writer.flush(); 
            return; 
        } 

        if(u<v){
            long diff = v-u; 
            long halfDiff = diff/2L; 
            long trial = u^halfDiff; 
            if(halfDiff + trial == v){
                writer.write(String.valueOf(2));
                writer.newLine();
                writer.write(String.valueOf(halfDiff));
                writer.write(" ");
                writer.write(String.valueOf(trial));
            } else {
                writer.write(String.valueOf(3));
                writer.newLine();
                writer.write(String.valueOf(halfDiff));
                writer.write(" ");
                writer.write(String.valueOf(halfDiff));
                writer.write(" ");
                writer.write(String.valueOf(u));
            }
             writer.flush(); 
        } else if(u == v){
            if(u>0){
                writer.write(String.valueOf(1));
                writer.newLine();
                writer.write(String.valueOf(u));
            } else {
                writer.write(String.valueOf(0));
            }
        } else {
            writer.write(String.valueOf(-1));
        }
        writer.flush(); 
        return; 

    }

}