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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Ribhav
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastReader in = new FastReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        DEhabTheXorcist solver = new DEhabTheXorcist();
        solver.solve(1, in, out);
        out.close();
    }

    static class DEhabTheXorcist {
        public void solve(int testNumber, FastReader s, PrintWriter out) {
            long xor = s.nextLong();
            long sum = s.nextLong();

            if (sum == xor && sum == 0L) {
                out.println(0);
                return;
            } else if (sum == xor) {
                out.println("1");
                out.println(sum);
                return;
            } else if (xor > sum) {
                out.println(-1);
                return;
            }

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

            long[] a = compute(sum, xor);
            if (a.length == 0) {
                long diff = (sum - xor) / 2L;
                out.println(3);
                out.println(xor + " " + diff + " " + diff);
            } else {
                out.println(2);
                out.println(a[0] + " " + a[1]);
            }
        }

        static long[] compute(long S, long X) {
            long A = (S - X) / 2L;
            long a = 0L, b = 0L;
            final int LONG_FIELD_SIZE = 8;

            // Traverse through all bits
            for (long i = 0; i < 8 * LONG_FIELD_SIZE; i++) {
                long Xi = (X & (1L << i));
                long Ai = (A & (1L << i));
                if (Xi == 0L && Ai == 0L) {
                    // Let us leave bits as 0.
                } else if (Xi == 0 && Ai > 0) {
                    a = ((1L << i) | a);
                    b = ((1L << i) | b);
                } else if (Xi > 0 && Ai == 0) {
                    a = ((1L << i) | a);
                } else {
//                System.out.println("Not Possible");
                    return new long[0];
                }
            }

//        System.out.println("a = " + a +"\nb = " + b);
            long[] ans = new long[2];
            ans[0] = a;
            ans[1] = b;
            return ans;
        }

    }

    static class FastReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private FastReader.SpaceCharFilter filter;

        public FastReader(InputStream stream) {
            this.stream = stream;
        }

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

        public long nextLong() {
            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;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

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

        }

    }
}