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.util.Scanner;

public class ProblemD {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		
		Scanner s = new Scanner(System.in);
		
		long u = s.nextLong();
		long v = s.nextLong();
		
		if(u > v) {
			System.out.println(-1);
		}
		
		else if(v == u) {
			
			if(u == 0)
				System.out.println(0);
			else {
				System.out.println(1);
				System.out.println(u);
			}
			
		}
		
		else {
			long diff = v - u;
			
			if(diff%2!=0) {
				System.out.println(-1);
			}
			
			else {
				long x = diff/2;
				
				if((u&x) == 0) {
					System.out.println(2);
					System.out.println((u+x)+" "+x);
				}
				
				else {
					System.out.println(3);
					System.out.println(u+" "+x+" "+x);
				}
			}
		}

	}

}