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.math.BigInteger;
import java.util.*;

public class Main {

	static long sx = 0, sy = 0, m = (long) (1e9 + 7);

	static ArrayList<pair>[] a;
	static int[][] dp;
	static long[] farr;
	static boolean b = true;
	// static HashMap<Long, Integer> hm = new HashMap<>();

	static TreeMap<Integer, Integer> hm = new TreeMap<>();
	public static PrintWriter out;
	static ArrayList<pair> ans = new ArrayList<>();
	static long[] fact = new long[(int) 1e6];
	static StringBuilder sb = new StringBuilder();
	static boolean cycle = false;
	static long mod = 998244353;

	public static void main(String[] args) throws IOException {

		Reader scn = new Reader();

		long xor = scn.nextLong(), sum = scn.nextLong();

//		pair rp = compute(sum, xor);

		if (xor == sum) {

			if (xor == 0) {
				System.out.println(0);
			}

			else {
				System.out.println(1);
				System.out.println(xor);
			}
		}

//		else if (rp != null) {
//			System.out.println(2);
//			System.out.println(rp.a + " " + rp.b);
//		}

		else {

			long rem = sum - xor;

			if (rem % 2 == 1 || rem < 0)
				System.out.println(-1);

			else {
//				System.out.println(3);
//				System.out.println(xor + " " + rem / 2 + " " + rem / 2);
				
				
				ArrayList<Long> p =new ArrayList<>();
				p.add(xor);
				p.add(rem/2);
				p.add(rem/2);
				
				if((p.get(0)&p.get(1))==0){
					
					System.out.println(2);
					System.out.println(p.get(0)+p.get(1)+" "+p.get(1));
				}
				
				else{
					System.out.println(3);
					System.out.println(p.get(0)+" "+p.get(1)+" "+p.get(1));
				}
			}

		}

	}

	static pair compute(long S, long X) {
		long A = (S - X) / 2;
		long a = 0, b = 0;
		final long LONG_FIELD_SIZE = 8;

		// Traverse through all bits
		for (long i = 0; i < 8 * LONG_FIELD_SIZE; i++) {
			long Xi = (X & (1 << i));
			long Ai = (A & (1 << i));
			if (Xi == 0 && Ai == 0) {
				// Let us leave bits as 0.
			} else if (Xi == 0 && Ai > 0) {
				a = ((1 << i) | a);
				b = ((1 << i) | b);
			} else if (Xi > 0 && Ai == 0) {
				a = ((1 << i) | a);

				// We leave i-th bit of b as 0.
			} else // (Xi == 1 && Ai == 1)
			{
				return null;
			}
		}

		pair rp = new pair();
		rp.a = a;
		rp.b = b;
		return rp;

	}

	// _________________________TEMPLATE_____________________________________________________________

	// private static int gcd(int a, int b) {
	// if (a == 0)
	// return b;
	//
	// return gcd(b % a, a);
	// }

	// static class comp implements Comparator<Integer> {
	//
	// @Override
	// public int compare(Integer o1, Integer o2) {
	//
	// return (int) (o2 - o1);
	// }
	//
	// }

	// public static long pow(long a, long b) {
	//
	// if(b<0)return 0;
	// if (b == 0 || b == 1)
	// return (long) Math.pow(a, b);
	//
	// if (b % 2 == 0) {
	//
	// long ret = pow(a, b / 2);
	// ret = (ret % mod * ret % mod) % mod;
	// return ret;
	// }
	//
	// else {
	// return ((pow(a, b - 1) % mod) * a % mod) % mod;
	// }
	// }

	private static class pair implements Comparable<pair> {

		long a, b;

		@Override
		public int compareTo(pair o) {

			return 1;
		}

	}

	public static class Reader {
		final private int BUFFER_SIZE = 1 << 16;
		private DataInputStream din;
		private byte[] buffer;
		private int bufferPointer, bytesRead;

		public Reader() {
			din = new DataInputStream(System.in);
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public Reader(String file_name) throws IOException {
			din = new DataInputStream(new FileInputStream(file_name));
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public String readLine() throws IOException {
			byte[] buf = new byte[1000000 + 1]; // line length
			int cnt = 0, c;
			while ((c = read()) != -1) {
				if (c == '\n')
					break;
				buf[cnt++] = (byte) c;
			}
			return new String(buf, 0, cnt);
		}

		public int nextInt() throws IOException {
			int ret = 0;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');

			if (neg)
				return -ret;
			return ret;
		}

		public long nextLong() throws IOException {
			long ret = 0;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');
			if (neg)
				return -ret;
			return ret;
		}

		public double nextDouble() throws IOException {
			double ret = 0, div = 1;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();

			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');

			if (c == '.') {
				while ((c = read()) >= '0' && c <= '9') {
					ret += (c - '0') / (div *= 10);
				}
			}

			if (neg)
				return -ret;
			return ret;
		}

		private void fillBuffer() throws IOException {
			bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
			if (bytesRead == -1)
				buffer[0] = -1;
		}

		private byte read() throws IOException {
			if (bufferPointer == bytesRead)
				fillBuffer();
			return buffer[bufferPointer++];
		}

		public void close() throws IOException {
			if (din == null)
				return;
			din.close();
		}

		public int[] nextIntArray(int n) throws IOException {
			int[] arr = new int[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextInt();
			}
			return arr;
		}

		public long[] nextLongArray(int n) throws IOException {
			long[] arr = new long[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextLong();
			}
			return arr;
		}

		public int[][] nextInt2DArray(int m, int n) throws IOException {
			int[][] arr = new int[m][n];
			for (int i = 0; i < m; i++) {
				for (int j = 0; j < n; j++)
					arr[i][j] = nextInt();
			}
			return arr;
		}
		// kickstart - Solution
		// atcoder - Main
	}

}