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 tr0 {
	static PrintWriter out;
	static StringBuilder sb;
	static long mod = 1000000007;
	static int inf = (int) 1e15;
	static ArrayList<Integer>[] ad;
	static int n;

	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		out = new PrintWriter(System.out);
		long a = sc.nextLong();
		long b = sc.nextLong();
		if (b < a) {
			System.out.println(-1);

			return;
		}
		if (a == b) {
			if(a==0) {
				System.out.println(0);
				return;
			}
			System.out.println(1);
			System.out.println(a);
			return;
		}
		ArrayList<Long> ele = new ArrayList<>();
		long sum = b - a;
		if (sum % 2 == 1) {
			System.out.println(-1);
			return;
		}
        long h=sum/2;
        if(((h|a)^a)==h) {
        	System.out.println(2);
        	System.out.println((a|h)+" "+((h|a)^a));
        }
        else {
        	System.out.println(3);
        	System.out.println(a+" "+h+" "+h);
        }
		out.flush();
	}

	static class seg implements Comparable<seg> {
		int a;
		int b;
		int id;

		seg(int aa, int bb, int vv) {
			a = aa;
			b = bb;
			id = vv;
		}

		public String toString() {
			return a + " " + b + " " + id;
		}

		public int compareTo(seg o) {
			if (a == o.a)
				return b - o.b;
			return a - o.a;
		}
	}

	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);
		}
	}
}