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:
//created by Whiplash99
import java.io.*;
import java.util.*;
public class D
{
    public static void main(String[] args) throws IOException
    {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));

        int i,N;

        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(1);
            }
            System.out.println(u);
            System.exit(0);
        }

        int count[]=new int[100];
        long list[]=new long[3];
        list[0]=u;
        v-=u;

        list[1]=list[2]=v/2;

        long pow[]=new long[100];
        pow[0]=1;
        for(i=1;i<60;i++)
            pow[i]=pow[i-1]*2;

        int max=0;
        for(i=0;i<3;i++)
        {
            for(int j=59;j>=0;j--)
            {
                if((pow[j]&list[i])!=0)
                {
                    count[j]++;
                    max=Math.max(max,count[j]);
                }
            }
        }

        long ans[][]=new long[max][60];
        for(i=0;i<max;i++)
        {
            for(int j=0;j<60;j++)
            {
                if(count[j]==0)
                    continue;
                ans[i][j]=1;
                count[j]--;
            }
        }

        ArrayDeque<Long> sol=new ArrayDeque<>();
        for(i=0;i<max;i++)
        {
            long tmp=0;
            for(int j=0;j<60;j++)
            {
                if(ans[i][j]==1)
                    tmp+=pow[j];
            }
            if(tmp!=0)
                sol.add(tmp);
        }

        StringBuilder sb=new StringBuilder();
        System.out.println(sol.size());
        for(long tmp:sol)
            sb.append(tmp).append(" ");
        sb.append("\n");
        System.out.println(sb);
    }
}