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 javax.sound.sampled.Line;
import java.io.*;
import java.math.BigInteger;
import java.util.*;

public class A {
    public static void main(String[] args) throws Throwable {
        long time = System.currentTimeMillis();

        Scanner sc = new Scanner();
        PrintWriter pw = new PrintWriter(System.out);

        long u = sc.nextLong();
        long v = sc.nextLong();

        if (u > v || (v - u) % 2 != 0)
            pw.println(-1);
        else {
            if (u == v) {
                if (u == 0)
                    pw.println(0);
                else {
                    pw.println(1);
                    pw.println(u);
                }
            } else {
                long dif = v - u;
                long x = u, y = 0;
                for (int i = 60; i >= 0; i--) {
                    long bit = (1L << i);
                    if ((u & bit) == 0 && dif >= 2 * bit) {
                        x |= bit;
                        y |= bit;
                        dif -= 2 * bit;
                    }
                }

                if (dif == 0) {
                    pw.println(2);
                    pw.println(x + " " + y);
                } else {
                    pw.println(3);
                    pw.println(u + " " + (v - u) / 2 + " " + (v - u) / 2);
                }
            }
        }

        pw.close();
        System.err.println((System.currentTimeMillis() - time) / 1000.0);
    }

    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        Scanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        Scanner(String s) throws Throwable {
            br = new BufferedReader(new FileReader(new File(s)));
        }

        String next() throws Throwable {
            if (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

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

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

    }

}