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.HashMap;
import java.util.Map;
import java.util.StringTokenizer;

/**
 * Created by Katushka on 11.03.2020.
 */
public class EhabAndXorcist {
    static int[] readArray(int size, InputReader in) {
        int[] a = new int[size];
        for (int i = 0; i < size; i++) {
            a[i] = in.nextInt();
        }
        return a;
    }

    static class Params {
        int xor;
        int sum;
        int a[];
        int resPeren;
        int peren;

        public Params(int xor, int sum, int[] a, int resPeren, int peren) {
            this.xor = xor;
            this.sum = sum;
            this.a = a;
            this.resPeren = resPeren;
            this.peren = peren;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;

            Params params = (Params) o;

            if (xor != params.xor) return false;
            if (sum != params.sum) return false;
            return peren == params.peren;
        }

        @Override
        public int hashCode() {
            int result = xor;
            result = 31 * result + sum;
            result = 31 * result + peren;
            return result;
        }
    }

    public static void main(String[] args) throws FileNotFoundException {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));

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

        if (xor == 0 && sum == 0) {
            out.println(0);
        } else if (xor == sum) {
            out.println(1);
            out.println(xor);
        } else if (xor > sum || (sum - xor) % 2 == 1){
            out.println(-1);
        } else {
            long a = (sum - xor) / 2;
            if (((xor  + a)^ a) == xor) {
                out.println(2);
                out.println((xor  + a) + " " + a);
            } else {
                out.println(3);
                out.println(xor + " " + a + ' ' + a);
            }
        }
        out.close();
    }


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

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

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public String nextString() {
            try {
                return reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public char nextChar() {
            return next().charAt(0);
        }
    }
}