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.*;
public class Main {
    public static void main(String args[])
    {
        FastReader input=new FastReader();
        PrintWriter out=new PrintWriter(System.out);
        int T=1;
        while(T-->0)
        {
            long u=input.nextLong();
            long v=input.nextLong();
            long w=v-u;
            if(w<0 || w%2!=0)
            {
                out.println(-1);
            }
            else
            {
                w=w/2;
                ArrayList<Long> list=new ArrayList<>();
                if((w&u)==0)
                {
                    long a=w+u;
                    if(a!=0)
                    {
                        list.add(a);
                    }
                    a=w;
                    if(a!=0)
                    {
                        list.add(a);
                    }
                }
                else
                {
                    if(u!=0)
                    {
                        list.add(u);
                    }
                    if(w!=0)
                    {
                        list.add(w);
                        list.add(w);
                    }
                }
                out.println(list.size());
                for(int i=0;i< list.size();i++)
                {
                    out.print(list.get(i)+" ");
                }
                out.println();
            }
        }
        out.close();
    }
    public static long power(long a,long b)
    {
        long res=1;
        while(b>0)
        {
            if(b%2!=0)
            {
                res=res*a;
            }
            b=b/2;
            a=a*a;
        }
        return res;
    }
    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;
        }
    }
}