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.*;
import java.io.*;

public class Solution {

	public static void main(String[] args) {
		// write your code here
		Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
		long u = in.nextLong(), v = in.nextLong();

		if (u == 0 && v == 0) {
			System.out.println(0);
			return;
		}

		if (u == v) {
			System.out.println(1);
			System.out.println(u);
			return;
		}

		if (u == 0) {
			if ((v & 1) == 1)
				System.out.println(-1);
			else {
				v /= 2;
				System.out.println(2);
				System.out.println(v + " " + v);
			}
			return;
		}

		long num = v - u;

		if (u > v || ((num) & 1) == 1) {
			System.out.println(-1);
			return;
		}

		num /= 2;

		if ((num & u) == 0) {
			System.out.println(2);
			System.out.println(num + " " + (u + num));
		} else {
			System.out.println(3);
			System.out.println(u + " " + num + " " + num);
		}
	}
}