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 EhabTheXorcist {
	public static void main(String[] args) throws IOException {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter out = new PrintWriter(System.out);
		StringTokenizer st = new StringTokenizer(in.readLine());
		long U = Long.parseLong(st.nextToken());
		long V = Long.parseLong(st.nextToken());
		if(U > V || (U & 1 ^ V & 1) > 0) {
			out.println(-1);
		} else if(U == V) {
			if(U == 0) {
				out.println(0);
			} else {
				out.println(1);
				out.println(V);
			}
		} else {
			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);
			}
		}
		in.close();
		out.close();
	}
}