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.*;
import java.util.*;

public class Main {
	static Scanner sc = new Scanner(System.in);
	static PrintWriter out = new PrintWriter(System.out);
	final static int INF = (int) 1e9;

	public static void main(String[] args) throws Exception {
		long xor = sc.nextLong(), sum = sc.nextLong();
		long a = xor, b = 0, c = 0;
		
		if(sum == 0) {
			System.out.println(0);
			return;
		}

		if (sum < xor) {
			System.out.println(-1);
			return;
		}
		if (sum == xor) {
			System.out.println(1);
			System.out.println(a);
			return;
		}

		sum -= xor;
		if (sum % 2 != 0) {
			System.out.println(-1);
			return;
		}

		sum /= 2;
		if ((a & sum) == 0) {
			a |= sum;
			b |= sum;
		} else {
			b |= sum;
			c |= sum;
		}

		if (c == 0) {
			out.println(2);
			out.println(a + " " + b);
		} else {
			out.println(3);
			out.println(a + " " + b + " " + c);
		}

		out.close();
	}

	static class Pair implements Comparable<Pair> {
		int u, v;

		Pair(int u, int v) {
			this.u = u;
			this.v = v;
		}

		public int compareTo(Pair o) {
			if (u == o.u)
				return v - o.v;
			return u - o.u;
		}
	}

}

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