Description:
Given 2 integers $$$u$$$ and $$$v$$$, find the shortest array such that bitwise-xor of its elements is $$$u$$$, and the sum of its elements is $$$v$$$.
Input Format:
The only line contains 2 integers $$$u$$$ and $$$v$$$ $$$(0 \le u,v \le 10^{18})$$$.
Output Format:
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.
Note:
In the first sample, $$$3\oplus 1 = 2$$$ and $$$3 + 1 = 4$$$. There is no valid array of smaller length.
Notice that in the fourth sample the array is empty.