No tag edit access

B. "Or" Game

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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.

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 *a*_{1}, *a*_{2}, ..., *a*_{n} (0 ≤ *a*_{i} ≤ 10^{9}).

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.

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Dec/17/2017 01:22:34 (c6).

Desktop version, switch to mobile version.

User lists

Name |
---|