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.Scanner; 
import java.util.StringTokenizer;
import java.util.*;
public class codeforcesD{
   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; 
        } 
    } 
    public static void main(String args[]){
        FastReader sc=new FastReader();
         
        long u=sc.nextLong();
        long v=sc.nextLong();
        boolean flag=true,print=false;
        if(u>v || (v-u)%2==1){flag=false;}
        if(u==v && u!=0){System.out.println("1");System.out.println(u);print=true;}
        if(u==0 && v==0){System.out.println("0");print=true;}
        if(flag && !print){
          long x=u;long y=v-u;
          if((x^y)==u){
              System.out.println("2");
              System.out.println(x+" "+y);flag=false;print=true;}
        }
        if(flag && !print){
              long x=(u+v)/2;long y=(v-u)/2;
              if((x^y)==u){System.out.println("2");
              System.out.println(x+" "+y);flag=false;print=true;}
            }    
        if(flag && !print){
            long x=u,y=(v-u)/2,z=(v-u)/2;
            if(((x^y)^z)==u){System.out.println("3");System.out.println(x+" "+y+" "+z);flag=false;print=true;}
        }    
        if(!print){System.out.println("-1");}
    }
}