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:
// Don't place your source in a package

import java.math.BigInteger;
import java.util.*;
import java.lang.*;
import java.io.*;



// Please name your class Main
public class Main {
    static FastScanner fs=new FastScanner();
    static class FastScanner {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st=new StringTokenizer("");
        public String next() {
            while (!st.hasMoreElements())
                try {
                    st=new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }
        int Int() {
            return Integer.parseInt(next());
        }

        long Long() {
            return Long.parseLong(next());
        }

        String Str(){
            return next();
        }
    }


    public static void main (String[] args) throws java.lang.Exception {
        PrintWriter out = new PrintWriter(System.out);


        int T=1;
        for(int t=0;t<T;t++){
            long u=Long();
            long v=Long();
            Solution sol=new Solution(out);
            sol.solution(u,v);
        }
        out.flush();

    }


    public static int Int(){
        return fs.Int();
    }
    public static long Long(){
        return fs.Long();
    }
    public static String Str(){
        return fs.Str();
    }

}






class Solution{
    PrintWriter out;
    public Solution(PrintWriter out){
        this.out=out;
    }




    public void solution(long xor,long sum){
        if(sum<xor){
            out.println(-1);
            return;
        }
        if(xor==sum){
            if(sum==0){
                out.println(0);
                return;
            }
            out.println(1);
            out.println(sum);
            return;
        }


        long dif=sum-xor;


        if(dif%2==0){
            long a=xor;
            long half=dif/2;
            boolean good=true;
            for(int i=0;i<63;i++){
                if((half&(1l<<i))!=0){
                    if((xor&(1l<<i))!=0){
                        good=false;
                    }
                }
            }
            if(good){
                for(int i=0;i<63;i++){
                    if((half&(1l<<i))!=0){
                        a=a|(1l<<i);
                    }
                }
                out.println(2);
                out.println(a+" "+half);
            }
            else{
                out.println(3);
                out.println(xor+" "+dif/2+" "+dif/2);
            }
        }
        else{
            out.println(-1);
        }

    }






}



/*
                             ;\
                            |' \
         _                  ; : ;
        / `-.              /: : |
       |  ,-.`-.          ,': : |
       \  :  `. `.       ,'-. : |
        \ ;    ;  `-.__,'    `-.|
         \ ;   ;  :::  ,::'`:.  `.
          \ `-. :  `    :.    `.  \
           \   \    ,   ;   ,:    (\
            \   :., :.    ,'o)): ` `-.
           ,/,' ;' ,::"'`.`---'   `.  `-._
         ,/  :  ; '"      `;'          ,--`.
        ;/   :; ;             ,:'     (   ,:)
          ,.,:.    ; ,:.,  ,-._ `.     \""'/
          '::'     `:'`  ,'(  \`._____.-'"'
             ;,   ;  `.  `. `._`-.  \\
             ;:.  ;:       `-._`-.\  \`.
              '`:. :        |' `. `\  ) \
      -hrr-      ` ;:       |    `--\__,'
                   '`      ,'
                        ,-'


                      free bug dog
*/