Ehab the Xorcist

题意翻译

给定整数 $u$ 和 $v(0\le u,v \le 10^{18})$，试构造长度最短的数组，使得数组内所有元素的异或和为 $u$，加和为 $v$。 如果有解，输出两行，第一行输出一个整数 $n$，第二行输出 $n$ 个非负整数，表示数组里的元素。多解输出任意一组即可。如果无解，输出一行一个整数 $-1$。

题目描述

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 $ .

输入输出格式

输入格式

The only line contains 2 integers $ u $ and $ v $ $ (0 \le u,v \le 10^{18}) $ .

输出格式

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.

输入输出样例

输入样例 #1

2 4

输出样例 #1

2
3 1

输入样例 #2

1 3

输出样例 #2

3
1 1 1

输入样例 #3

8 5

输出样例 #3

-1

输入样例 #4

0 0

输出样例 #4

0

说明

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.