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A13302. Ehab the Xorcist

编程题 普及/提高-

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 #1
2 4
输出 #1
2
3 1
输入 #2
1 3
输出 #2
3
1 1 1
输入 #3
8 5
输出 #3
-1
输入 #4
0 0
输出 #4
0

说明/提示

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.
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