CF578B."Or" Game

普及/提高-

通过率：0%

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题目描述

You are given $n$ numbers $a_{1},a_{2},...,a_{n}$ . You can perform at most $k$ operations. For each operation you can multiply one of the numbers by $x$ . We want to make as large as possible, where denotes the bitwise OR.

Find the maximum possible value of after performing at most $k$ operations optimally.

输入格式

The first line contains three integers $n$ , $k$ and $x$ ( $1<=n<=200000$ , $1<=k<=10$ , $2<=x<=8$ ).

The second line contains $n$ integers $a_{1},a_{2},...,a_{n}$ ( $0<=a_{i}<=10^{9}$ ).

输出格式

Output the maximum value of a bitwise OR of sequence elements after performing operations.

输入输出样例

输入#1
```
3 1 2
1 1 1
```
输出#1
```
3
```
输入#2
```
4 2 3
1 2 4 8
```
输出#2
```
79
```

说明/提示

For the first sample, any possible choice of doing one operation will result the same three numbers $1$ , $1$ , $2$ so the result is .

For the second sample if we multiply $8$ by $3$ two times we'll get $72$ . In this case the numbers will become $1$ , $2$ , $4$ , $72$ so the OR value will be $79$ and is the largest possible result.

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