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.*;
import java.util.*;
import java.math.*;
public class Euler {

	static FastReader in;
	static PrintWriter o;

	public static void solve() {
		long u = in.nextLong();
		long v = in.nextLong();
		if (u > v || u % 2 != v % 2) {
			o.println("-1");
		} else if (u == v && u == 0) {
			o.println("0");
		} else if (u == v) {
			o.println("1");
			o.println(u);
		} else {
			long x = (v - u) / 2;
			if ((x & u) == 0) {
				o.println("2");
				o.println((u+x) + " " + x);
			} else {
				o.println("3");
				o.println(u + " " + x + " " + x);
			}
		}
		o.close();
		return;
	}

	public static void main(String[] args) {
		in = new FastReader();
		o = new PrintWriter(System.out);
		solve();
		return;
	}

	static class FastReader {
		BufferedReader br;
		StringTokenizer st;

		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String next() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

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

		long nextLong() {
			return Long.parseLong(next());
		}

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

		int[] readArray(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++) a[i] = nextInt();
			return a;
		}

		long[] readLongArray(int n) {
			long[] a = new long[n];
			for (int i = 0; i < n; i++) a[i] = nextLong();
			return a;
		}

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}
	}

}