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 a {
    public static void main(String[] args) throws IOException {
        FastReader scan = new FastReader();
        //PrintWriter out = new PrintWriter(new BufferedWriter(new FileWriter("taming.out")));
        PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        Task solver = new Task();
        //int t = scan.nextInt();
        int t = 1;
        for(int i = 1; i <= t; i++) solver.solve(i, scan, out);
        out.close();
    }
    static class Task {
        public void solve(int testNumber, FastReader sc, PrintWriter pw) {
        	long n = sc.nextLong();
        	long m = sc.nextLong();
        	if(n>m){
        		pw.println(-1);
        		return;
        	}
        	else if(m==0&&n==0){
        		pw.println(0);
        	}
        	else if(m==n){
        		pw.println(1);
        		pw.println(m);
        	}
        	else if((m-n)%2==1){
        		pw.println(-1);
        	}
        	else if((((m-n)>>1)^n)==((m-n)>>1)+n){
        		pw.println(2);
        		pw.println((((m-n)>>1))+n+" "+(((m-n)>>1)));
        		//pw.println(((((m-n)>>1))+n)^(((m-n)>>1)));
        	}
        	else{
        		pw.println(3);
        		pw.println((n)+" "+(m-n)/2+" "+((m-n)/2));
        		//pw.println((n)^(m-n)/2^((m-n)/2));
        	}
        	
        }

    }
    static class tup implements Comparable<tup>{
        int a, b,c;
        tup(){};
        tup(int a, int b, int c){
            this.a=a;
            this.b=b;
            this.c=c;
        }

        @Override
        public int compareTo( tup o2) {
            return o2.b!=b?Integer.compare(o2.b,b):Integer.compare(o2.a,a);
        }
    }
    static void shuffle(long[] a) {
        Random get = new Random();
        for (int i = 0; i < a.length; i++) {
            int r = get.nextInt(a.length);
            long temp = a[i];
            a[i] = a[r];
            a[r] = temp;
        }
    }
    static void shuffle(int[] a) {
        Random get = new Random();
        for (int i = 0; i < a.length; i++) {
            int r = get.nextInt(a.length);
            int temp = a[i];
            a[i] = a[r];
            a[r] = temp;
        }
    }
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

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

        public FastReader(String s) throws FileNotFoundException {
            br = new BufferedReader(new FileReader(new File(s)));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

}