Codeforces Round #320 (Div. 2) [Bayan Thanks-Round] D. "Or" Game 贪心

D. "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 ≤ 200 000, 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.

Sample test(s)

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.

题意，给出一个数列，要求，可以选k个数，乘上x,要求最终|的最大值。

贪心，最终的结果，一定是，某一个数乘上所有的x,其它数不变，因为，最大值最大，结果也会更大。