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#F1566. "Or" Game

    ID: 1572 传统题 2000ms 256MiB 尝试: 0 已通过: 0 难度: 5 上传者: 标签>枚举贪心算法思想进阶难度共享题库Codeforces英文题面题目来源题面语言

"Or" Game

题目描述

B. "Or" Game
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given n numbers a1,a2,...,an. 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.

Input

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 a1,a2,...,an (0≤ai≤109).

Output

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

Examples
Input
3 1 2
1 1 1
Output
3
Input
4 2 3
1 2 4 8
Output
79
Note

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.

题目来源：fps-www.educg.net-codeforce-1-2833.xml.zip；FPS 共享题包，题包内第 1086 题。保留原作者与原赛事署名。