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.awt.Point;
import java.io.*;
import java.util.*;
public class Main {
	static PrintWriter out;
	static Scanner sc;
	static ArrayList<Integer> primes;
	static boolean[] isComposite;
	public static void main(String[] args) throws Exception {
		// TODO Auto-generated method stub
		sc = new Scanner(System.in);
		out = new PrintWriter(System.out);
		long u = sc.nextLong();
		long v = sc.nextLong();
		if(u == v && v == 0) {
			out.println(u);
			out.flush();return;
		}else if(u == v) {
			out.println(1);
			out.println(u);
			out.flush();
			return;			
		}
		if(u>v)
			out.println(-1);
		else {
			long w = v-u;
			if((w&1) == 0) {
				long z = w>>1;
				if(((z+u)^z) == u) {
					out.println(2);
					out.println(z+" "+(u+z));
				}else {
					out.println(3);
					out.println(z+" "+z+" "+u);
				}
			}else {
				out.println(-1);
			}
		}
		out.flush();
	}
	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}

		public Scanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}

		public char nextChar() throws IOException {
			return next().charAt(0);
		}

		public Long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}
	}

}