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, 72so the OR value will be 79 and is the largest possible result.
#include
#include
#include
using namespace std;
const int maxn=2e5+100;
__int64 pre[maxn],back[maxn],a[maxn];
int main()
{
int i,n,k,x,num;
__int64 ans;
cin>>n>>k>>x;
for(i=1;i<=n;i++) {
cin>>a[i];
pre[i]=a[i]|pre[i-1];
}
num=1;
while(k--) num*=x;
for(i=n;i>=0;i--) back[i]=a[i]|back[i+1];
ans=0;
for(i=1;i<=n;i++) {
ans=max(ans,pre[i-1]|(a[i]*num|back[i+1]));
}
cout<
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