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 MainClass
{
    public static void main(String[] args)throws IOException
    {
        Reader in = new Reader();
        long u = in.nextLong();
        long v = in.nextLong();
        if (v < u)
        {
            System.out.println(-1);
            System.exit(0);
        }
        else if (u == v && u == 0)
        {
            System.out.println(0);
            System.exit(0);
        }
        long n1 = 0L;
        long n2 = 0L;
        long req = v - u;
        long uu = u;

        for (int i=60;i>=0;i--)
        {
            long mask = 1L << i;
            if ((mask & u) > 0)
                continue;

            mask *= 2;
            if (req >= mask)
            {
                req -= mask;
                u |= (1L << i);
                n1 |= (1L << i);
            }
        }

        ArrayList<Long> vcc = new ArrayList<>();
        if (req == 0)
        {
            vcc.add(u);
            if (n1 > 0)
                vcc.add(n1);
            System.out.println(vcc.size());
            for (int i=0;i<vcc.size();i++)
                System.out.print(vcc.get(i) + " ");
            System.exit(0);
        }

        req = v - uu;
        n1 = 0L;
        n2 = 0L;
        for (int i=60;i>=0;i--)
        {
            long mask = 1L << i;
            if ((mask & uu) > 0)
            {
                mask *= 2;
                if (req >= mask)
                {
                    req -= mask;
                    n2 |= (1L << i);
                    n1 |= (1L << i);
                }
            }
            else
            {
                mask *= 2;
                if (req >= mask)
                {
                    req -= mask;
                    uu |= (1L << i);
                    n1 |= (1L << i);
                }
            }
        }
        if (req > 0)
        {
            System.out.println(-1);
            System.exit(0);
        }
        vcc.clear();
        vcc.add(uu);
        if (n1 > 0)
            vcc.add(n1);
        if (n2 > 0)
            vcc.add(n2);
        System.out.println(vcc.size());
        for (int i=0;i<vcc.size();i++)
            System.out.print(vcc.get(i) + " ");
    }
}
class Reader
{
    final private int BUFFER_SIZE = 1 << 16;
    private DataInputStream din;
    private byte[] buffer;
    private int bufferPointer, bytesRead;

    public Reader()
    {
        din = new DataInputStream(System.in);
        buffer = new byte[BUFFER_SIZE];
        bufferPointer = bytesRead = 0;
    }

    public Reader(String file_name) throws IOException
    {
        din = new DataInputStream(new FileInputStream(file_name));
        buffer = new byte[BUFFER_SIZE];
        bufferPointer = bytesRead = 0;
    }

    public String readLine() throws IOException
    {
        byte[] buf = new byte[64]; // line length
        int cnt = 0, c;
        while ((c = read()) != -1)
        {
            if (c == '\n')
                break;
            buf[cnt++] = (byte) c;
        }
        return new String(buf, 0, cnt);
    }

    public int nextInt() throws IOException
    {
        int ret = 0;
        byte c = read();
        while (c <= ' ')
            c = read();
        boolean neg = (c == '-');
        if (neg)
            c = read();
        do
        {
            ret = ret * 10 + c - '0';
        }  while ((c = read()) >= '0' && c <= '9');

        if (neg)
            return -ret;
        return ret;
    }

    public long nextLong() throws IOException
    {
        long ret = 0;
        byte c = read();
        while (c <= ' ')
            c = read();
        boolean neg = (c == '-');
        if (neg)
            c = read();
        do {
            ret = ret * 10 + c - '0';
        }
        while ((c = read()) >= '0' && c <= '9');
        if (neg)
            return -ret;
        return ret;
    }

    public double nextDouble() throws IOException
    {
        double ret = 0, div = 1;
        byte c = read();
        while (c <= ' ')
            c = read();
        boolean neg = (c == '-');
        if (neg)
            c = read();

        do {
            ret = ret * 10 + c - '0';
        }
        while ((c = read()) >= '0' && c <= '9');

        if (c == '.')
        {
            while ((c = read()) >= '0' && c <= '9')
            {
                ret += (c - '0') / (div *= 10);
            }
        }

        if (neg)
            return -ret;
        return ret;
    }

    private void fillBuffer() throws IOException
    {
        bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
        if (bytesRead == -1)
            buffer[0] = -1;
    }

    private byte read() throws IOException
    {
        if (bufferPointer == bytesRead)
            fillBuffer();
        return buffer[bufferPointer++];
    }

    public void close() throws IOException
    {
        if (din == null)
            return;
        din.close();
    }
}