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:
// package com.company.codeforces;


import java.util.*;

public class Solution {


    public static void main(String[] args) {
        Scanner input = new Scanner(System.in);
        long u = input.nextLong();
        long v = input.nextLong();

        //(a&b)=(a+b-a^b)/2
        if (u == v) {
            if (u > 0) {
                System.out.println(1);
            }
            System.out.println(u);
        } else {
            if ((v - u) % 2 != 0 || u > v) {
                System.out.println(-1);
            } else {
                long x = ((v - u) / 2);
                if ((x ^ u) == x + u) {
                    System.out.println(2);
                    System.out.println(x + u + " " + x);
                } else {
                    System.out.println(3);
                    System.out.println(u + " " + x + " " + x);
                }
            }


        }
    }
}
//10 1 1