A10017. "Or" Game

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.

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 $a_{1},a_{2},...,a_{n}$ ( $0<=a_{i}<=10^{9}$ ).

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

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.