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:
//                I know stuff but probably my rating tells otherwise...

//               Kya hua, code samajhne ki koshish kar rhe ho?? Mat karo,
//                      mujhe bhi samajh nhi aata kya likha hai


import java.io.*;
import java.util.*;

import static java.lang.Math.*;

public class _1325D {

    static void Mangni_ke_bail_ke_dant_na_dekhal_jye() {
        long n = nl(), m = nl(); long w = m - n;
        if (n == 0 && m == 0) pl(0);
        else if (n > m) pl(-1);
        else if (((m - n) & 1) == 1) pl(-1);
        else if (n == m) pl("1\n" + n);
        else if ((n & (w >>= 1)) != 0) pl("3\n" + w + " " + w + " " + n);
        else pl("2\n" + w + " " + (n ^ w));
    }


    //----------------------------------------The main code ends here------------------------------------------------------
    /*-------------------------------------------------------------------------------------------------------------------*/
    //-----------------------------------------Rest's all dust-------------------------------------------------------------


    static int mod9 = 1_000_000_007;
    static int n, m, l, k, t;
    static AwesomeInput input;
    static PrintWriter pw;

    static long power(long a, long b) {
        long x = max(a, b);
        if (b == 0) return 1;
        if ((b & 1) == 1) return a * power(a * a, b >> 1);
        return power(a * a, b >> 1);
    }

    // The Awesome Input Code is a fast IO method //
    static class AwesomeInput {
        private InputStream letsDoIT;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;

        private AwesomeInput(InputStream incoming) {
            this.letsDoIT = incoming;
        }

        public int read() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = letsDoIT.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        private long ForLong() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));
            return res * sgn;
        }

        private String ForString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            }
            while (!isSpaceChar(c));

            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            boolean isSpaceChar(int ch);
        }
    }

    // functions to take input//
    static int ni() {
        return (int) input.ForLong();
    }

    static String ns() {
        return input.ForString();
    }

    static long nl() {
        return input.ForLong();
    }

    //functions to give output
    static void pl() {
        pw.println();
    }

    static void p(Object o) {
        pw.print(o + " ");
    }

    static void pws(Object o) {
        pw.print(o + "");
    }

    static void pl(Object o) {
        pw.println(o);
    }

    // Fast Sort is Radix Sort
    public static int[] fastSort(int[] f) {
        int n = f.length;
        int[] to = new int[n];
        {
            int[] b = new int[65537];
            for (int i = 0; i < n; i++) b[1 + (f[i] & 0xffff)]++;
            for (int i = 1; i <= 65536; i++) b[i] += b[i - 1];
            for (int i = 0; i < n; i++) to[b[f[i] & 0xffff]++] = f[i];
            int[] d = f;
            f = to;
            to = d;
        }
        {
            int[] b = new int[65537];
            for (int i = 0; i < n; i++) b[1 + (f[i] >>> 16)]++;
            for (int i = 1; i <= 65536; i++) b[i] += b[i - 1];
            for (int i = 0; i < n; i++) to[b[f[i] >>> 16]++] = f[i];
            int[] d = f;
            f = to;
            to = d;
        }
        return f;
    }

    public static void main(String[] args) {      //threading has been used to increase the stack size.
        try {
            input = new AwesomeInput(System.in);
            pw = new PrintWriter(System.out, true);
            input = new AwesomeInput(new FileInputStream("/home/saurabh/Desktop/input.txt"));
            pw = new PrintWriter(new BufferedWriter(new FileWriter("/home/saurabh/Desktop/output.txt")), true);

        } catch (Exception e) {
        }

        new Thread(null, null, "AApan_gand_hawai_dusar_ke_kare_dawai", 1 << 25)  //the last parameter is stack size desired.
        {
            public void run() {
                try {
                    double s = System.currentTimeMillis();
                    Mangni_ke_bail_ke_dant_na_dekhal_jye();
                    //System.out.println(("\nExecution Time : " + ((double) System.currentTimeMillis() - s) / 1000) + " s");
                    pw.flush();
                    pw.close();
                } catch (Exception e) {
                    e.printStackTrace();
                    System.exit(1);
                }
            }
        }.start();
    }
}