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 18bce002
 */
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 w) {
            long u = s.nextLong(), v = s.nextLong();
            if (u % 2 != v % 2 || u > v) {
                w.println(-1);
                return;
            }
            if (v == 0 && u == 0) {
                w.println(0);
                return;
            }
            if (v == u) {
                w.println(1);
                w.println(v);
                return;
            }
            if (((u + (v - u) / 2) ^ ((v - u) / 2)) == u) {
                w.println(2);
                w.println(u + (v - u) / 2 + " " + (v - u) / 2);
            } else {
                w.println(3);
                w.println((v - u) / 2 + " " + (v - u) / 2 + " " + u);
            }
        }
 
    }
 
    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 c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
 
        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
 
        }
 
    }
}