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.*;

public class Main {
    static FastScanner in = new FastScanner();


    public static void main(String[] args) throws IOException {
        long a = in.nextLong();
        long b = in.nextLong();
        if (a + b == 0) in.out.println(0);
        else {
            if (a > b || a % 2 != b % 2) in.out.println(-1);
            else {
                if (a == b) {
                    in.out.println(1);
                    in.out.println(a);
                } else {
                    long x = (b - a) >> 1;
                    if ((x & a) == 0) {
                        in.out.println(2);
                        in.out.println(a + x + " " + x);
                    } else {
                        in.out.println(3);
                        in.out.println(a + " " + x + " " + x);
                    }
                }
            }
        }
        in.out.close();
    }
}

class FastScanner {
    BufferedReader br;
    StringTokenizer st = new StringTokenizer("");
    PrintWriter out;

    FastScanner() {
        br = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
    }

    FastScanner(String in, String out_) throws FileNotFoundException {
        br = new BufferedReader(new FileReader(in));
        out = new PrintWriter(out_);
    }

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

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

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