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 TestClass {
 
	static PrintWriter out = new PrintWriter(System.out);
	public static void main(String[] args) throws IOException{
 
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		String s1[] = in.readLine().split(" ");
		long u = Long.parseLong(s1[0]);
		long v = Long.parseLong(s1[1]);
		if(u>v) {
			out.println("-1");
		}
		else if(u==v) {
			if(u==0)
			{
				out.println(u);
			}
			else {
				out.println("1");
				out.println(u);
			}
		}
		else {
			if((v-u)%2==0) {
				long x = (v-u)/2;
				if((x&u)==0) {
					out.println("2");
					out.println((u+x)+" "+x);
				}
				else {
					out.println("3");
					out.println(u+" "+x+" "+x);
				}
			}
			else {
				out.println("-1");
			}
		}
        out.close();
	}	
	
}