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.Comparator;
import java.util.StringTokenizer;

/*
 * To change this license header, choose License Headers in Project Properties.
 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */

/**
 *
 * @author User
 */
public class CF_628D 
{
    static class FastReader {
        
        BufferedReader br;
        StringTokenizer st;
        
        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
        
        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        
        int nextInt() {
            return Integer.parseInt(next());
        }
        
        long nextLong() {
            return Long.parseLong(next());
        }
        
        double nextDouble() {
            return Double.parseDouble(next());
        }
        
        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

    static class Var {

        int a, b;

        Var(int x, int y) {
            a = x;
            b = y;
        }
    }
    
    static class Comp implements Comparator<Var> {

        public int compare(Var o1, Var o2) {
            if (o1.b < o2.b) {
                return 1;
            } else {
                return -1;
            }
        }
    }
    static boolean even(long n)
    {
        return (n%2==0);
    }
    public static void main(String[] args) {
        FastReader sc = new FastReader();
        int t = 1;
        while(t-->0)
        {
            long u=sc.nextLong();
            long v=sc.nextLong();
            if(u>v)
            {
                System.out.println(-1);
                return;
            }
            if(u==v)
            {
                if(u!=0)
                {
                    System.out.println("1");
                    System.out.println(u);
                }
                else
                    System.out.println("0");
                return;
            }
            
            
            if(even(v-u))
            {                
                long ab=(v-u)/2L;
                //System.out.println("ab="+ab);
                if((u&ab)==0L)
                {
                    //System.out.println("yes");
                    long a=u|ab;
                    long b=a^u;
                    System.out.println("2");
                    System.out.println(a+" "+b);
                    return;
                }
            }
            if(v>2 && even(v-u))
            {
                long x=(v-u)/2;
                System.out.println("3");
                System.out.println(x+" "+x+" "+u);
                return;
            }
            System.out.println("-1");
        }
    }
}