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 code12 {

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

}