CF1325D Ehab the Xorcist

Description

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 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.

Explanation/Hint

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.