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.PrintWriter;
import java.util.*;
public class test2 {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		long u = sc.nextLong();
		long v = sc.nextLong();
		if(v>0&&u>0 && v-u>0 && (v-u)%2==0) {
		
			long a = u;
			long b = (v-u)/2;
			long c = b;
			if((a+b)==(a|b)) {
				pw.println(2);
				pw.println(a+b + " " + b);
			}else {
				pw.println(3);
				pw.println(a + " " + b + " " + c);
			}
			
		}else if(u==0 && v-u>0 &&  (v-u)%2==0)  {
			pw.println(2);
			pw.println((v-u)/2 + " " + (v-u)/2);
		}else if(v-u==0 && u>0) {
			pw.println(1);
			pw.println(v);
		}else if(v==0 && u==0)
			pw.println(0);
		else{
			pw.println(-1);
		}
		pw.flush();
		pw.close();
	}
}
class Pair {
	int a,b;
	public Pair(int a,int b) {
		this.a = a;
		this.b = b;
	}
}