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.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class Round628D {

	public static void solve() {
		long u = s.nextLong();
		long v = s.nextLong();
		if(u == v && u == 0) {
			out.println(0);
		}else if(u == v ){
			out.println(1);
			out.println(u);
		}else if((u&(1)) != (v&1) || u > v){
			out.println(-1);
		}else {
			ArrayList<Long> ans = new ArrayList<Long>();
			boolean check = Recur(u, v, 0, 0, Integer.max(Long.toBinaryString(u).length(), Long.toBinaryString(v).length()), ans);
			if(check) {
				out.println(ans.size());
				for(int i = 0; i < ans.size(); i++) {
					out.print(ans.get(i)+" ");
				}
			}else {
				out.println(-1);
			}
		}
	}

	public static int[] numbers = { 0, 1, 3, 7};
	
	public static boolean Recur(long u, long v, long carry, int pos, int n, ArrayList<Long> ans) {
		if(pos == n) {
			if(carry == 0)return true;
			else return false;
		}
		if((carry&1) == 1) {
			if((u&(1L<<pos)) > 0) {
				if((v&(1L<<pos))>0) {
					return false;
				}else {
					for(int on = 1; on <= 3; on+=2) {
						if(on > ans.size()) {
							while(on != ans.size()) {
								ans.add(0L);
							}
						}
						for(int i = 0; i < on; i++) {
							long val = ans.get(i);
							ans.set(i, val|(1L<<pos));
						}
						boolean check = Recur(u, v, ((carry+on)>>1), pos+1, n, ans);
						if(check) {
							return true;
						}
					}
				}
			}else {
				if((v&(1L<<pos))>0) {
					for(int on = 0; on <= 2; on+=2) {
						if(on > ans.size()) {
							while(on != ans.size()) {
								ans.add(0L);
							}
						}
						for(int i = 0; i < on; i++) {
							long val = ans.get(i);
							ans.set(i, val|(1L<<pos));
						}
						boolean check = Recur(u, v, ((carry+on)>>1), pos+1, n, ans);
						if(check) {
							return true;
						}
					}
				}else {
					return false;
				}
			}
		}else {
			if((u&(1L<<pos)) > 0) {
				if((v&(1L<<pos))> 0) {
					for(int on = 1; on <= 3; on+=2) {
						if(on > ans.size()) {
							while(on != ans.size()) {
								ans.add(0L);
							}
						}
						for(int i = 0; i < on; i++) {
							long val = ans.get(i);
							ans.set(i, val|(1L<<pos));
						}
						boolean check = Recur(u, v, ((carry+on)>>1), pos+1, n, ans);
						if(check) {
							return true;
						}
					}
				}else {
					return false;
				}
			}else {
				if((v&(1L<<pos))>0) {
					return false;
				}else {
					for(int on = 0; on <= 2; on+=2) {
						if(on > ans.size()) {
							while(on != ans.size()) {
								ans.add(0L);
							}
						}
						for(int i = 0; i < on; i++) {
							long val = ans.get(i);
							ans.set(i, val|(1L<<pos));
						}
						boolean check = Recur(u, v, ((carry+on)>>1), pos+1, n, ans);
						if(check) {
							return true;
						}
					}
				}
			}
		}
		return false;
	}
	
	public static void main(String[] args) {
		out = new PrintWriter(new BufferedOutputStream(System.out));
		s = new FastReader();
		solve();
		out.close();
	}

	public static FastReader s;
	public static PrintWriter out;

	public static class FastReader {
		BufferedReader br;
		StringTokenizer st;

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

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

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

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

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

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

	
}