#include <bits/stdc++.h>
using namespace std;
long long n, k, x;
int main() {
  ios_base::sync_with_stdio(false);
  cin >> n >> k >> x;
  long long a[n], mx = INT_MIN;
  map<long long, int, greater<long long>> m, m1;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    long long bb = 1;
    while (bb <= a[i]) {
      if (bb & a[i]) m[bb]++;
      bb *= 2;
    }
  }
  vector<long long> shifts;
  long long bit = m.begin()->first;
  for (int i = 0; i < n; i++)
    if (bit & a[i] || ((bit / 2) & a[i])) shifts.push_back(i);
  long long ans = 0;
  for (int i = 0; i < shifts.size(); i++) {
    m1 = m;
    bit = 1;
    while (bit <= a[shifts[i]]) {
      if (bit & a[shifts[i]]) m1[bit]--;
      bit *= 2;
    }
    long long temp = 0;
    for (auto it = m1.begin(); it != m1.end(); it++)
      if (it->second > 0) temp += (it->first);
    long long cu = a[shifts[i]];
    for (int kk = 0; kk < k; kk++) cu *= x;
    temp = temp | cu;
    ans = max(temp, ans);
  }
  cout << ans;
  return 0;
}

### Prompt

Please create a solution in CPP to the following problem:

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 <image> as large as possible, where <image> denotes the bitwise OR. 

Find the maximum possible value of <image> 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.

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 <image>. 

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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
long long n, k, x;
int main() {
  ios_base::sync_with_stdio(false);
  cin >> n >> k >> x;
  long long a[n], mx = INT_MIN;
  map<long long, int, greater<long long>> m, m1;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    long long bb = 1;
    while (bb <= a[i]) {
      if (bb & a[i]) m[bb]++;
      bb *= 2;
    }
  }
  vector<long long> shifts;
  long long bit = m.begin()->first;
  for (int i = 0; i < n; i++)
    if (bit & a[i] || ((bit / 2) & a[i])) shifts.push_back(i);
  long long ans = 0;
  for (int i = 0; i < shifts.size(); i++) {
    m1 = m;
    bit = 1;
    while (bit <= a[shifts[i]]) {
      if (bit & a[shifts[i]]) m1[bit]--;
      bit *= 2;
    }
    long long temp = 0;
    for (auto it = m1.begin(); it != m1.end(); it++)
      if (it->second > 0) temp += (it->first);
    long long cu = a[shifts[i]];
    for (int kk = 0; kk < k; kk++) cu *= x;
    temp = temp | cu;
    ans = max(temp, ans);
  }
  cout << ans;
  return 0;
}

```