"Or" Game

题意翻译

现在有n个数$a_1,a_2,a_3,...,a_n$ 。你最多可以进行k次操作，每次操作你可以将其中一个数乘以$x$ 。找出使得$a_1|a_2|...|a_n$ 最大的方法，”|“代表位或。

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.

输入输出格式

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

输入样例 #1

3 1 2
1 1 1

输出样例 #1

3

输入样例 #2

4 2 3
1 2 4 8

输出样例 #2

79

说明

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.