#include <bits/stdc++.h>
using namespace std;
unsigned long long dp[200000 + 1][10 + 1];
int main() {
  ios_base::sync_with_stdio(false);
  unsigned long long n, k, x;
  cin >> n >> k >> x;
  unsigned long long a[n + 1];
  for (int i = 1; i <= n; i++) cin >> a[i];
  unsigned long long max1 = 0;
  for (int itera = 0; itera <= 100; itera++) {
    double cur = clock() * 1.0 / CLOCKS_PER_SEC;
    if (cur > 1.75) break;
    random_shuffle(a + 1, a + n + 1);
    for (int i = 0; i <= n; i++)
      for (int j = 0; j <= k; j++) dp[i][j] = 0;
    for (int i = 1; i <= n; i++) {
      for (int j = 0; j <= k; j++) {
        unsigned long long po = 1;
        for (int k1 = 0; k1 <= j; k1++) {
          dp[i][j] = max(dp[i][j], ((a[i] * po) | dp[i - 1][j - k1]));
          po = po * x;
        }
      }
    }
    for (int i = 0; i <= k; i++) max1 = max(max1, dp[n][i]);
  }
  cout << max1;
  return 0;
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

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;
unsigned long long dp[200000 + 1][10 + 1];
int main() {
  ios_base::sync_with_stdio(false);
  unsigned long long n, k, x;
  cin >> n >> k >> x;
  unsigned long long a[n + 1];
  for (int i = 1; i <= n; i++) cin >> a[i];
  unsigned long long max1 = 0;
  for (int itera = 0; itera <= 100; itera++) {
    double cur = clock() * 1.0 / CLOCKS_PER_SEC;
    if (cur > 1.75) break;
    random_shuffle(a + 1, a + n + 1);
    for (int i = 0; i <= n; i++)
      for (int j = 0; j <= k; j++) dp[i][j] = 0;
    for (int i = 1; i <= n; i++) {
      for (int j = 0; j <= k; j++) {
        unsigned long long po = 1;
        for (int k1 = 0; k1 <= j; k1++) {
          dp[i][j] = max(dp[i][j], ((a[i] * po) | dp[i - 1][j - k1]));
          po = po * x;
        }
      }
    }
    for (int i = 0; i <= k; i++) max1 = max(max1, dp[n][i]);
  }
  cout << max1;
  return 0;
}

```