CF1325D.Ehab the Xorcist

普及/提高-

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题目描述

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 $v$ .

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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