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 CF_Ehab_and_Xorcist {

    public static void solve(InputReader in, PrintWriter out) throws Exception {

        long xor = in.nextLong();
        long sum = in.nextLong();




        if(xor>sum || ((xor%2) + (sum%2))%2!=0)
        {
            out.println(-1);
            return;
        }

        if(xor==0 &&  sum==0)
        {
            out.println(0);
            return;
        }

        if(sum==xor){
            out.println(1);
            out.println(xor);
            return;
        }

        long x = (sum-xor)/2;


        if((x & xor)==0)
        {
            out.println(2);
            out.println((x+xor)+" "+x);
        }

        else
        {
            out.println(3);
            out.println((xor)+" "+x+" "+x);
        }

    }

    /////////////////////////////////////////////////////////


    private final static long hash(long x, long y) {
        x += offset;
        y += offset;
        return x << 32 | y;
    }

    private final static int offset = (int) 3e5;

    public static void main(String[] args) throws Exception {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        solve(in, out);
        out.close();
    }

    static class InputReader {
        private BufferedReader reader;
        private StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        private String nextToken() throws IOException {
            while (tokenizer == null || !tokenizer.hasMoreTokens())
                tokenizer = new StringTokenizer(reader.readLine());
            return tokenizer.nextToken();
        }

        public String nextLine() throws IOException {
            return reader.readLine();
        }

        public int nextInt() throws IOException {
            return Integer.parseInt(nextToken());
        }

        public long nextLong() throws IOException {
            return Long.parseLong(nextToken());
        }

        public double nextDouble() throws IOException {
            return Double.parseDouble(nextToken());
        }

    }
}