Input Format


N K
a_1 a_2 a_3 ... a_N


Output Format

Print the minimum cost in one line. In the end put a line break.


Constraints

* 1 ≤ K ≤ N ≤ 15
* 1 ≤ a_i ≤ 10^9



Scoring

Subtask 1 [120 points]


* N = K

Subtask 2 [90 points]


* N ≤ 5
* a_i ≤ 7

Subtask 3 [140 points]


* There are no additional constraints.

Output Format

Print the minimum cost in one line. In the end put a line break.


Constraints

* 1 ≤ K ≤ N ≤ 15
* 1 ≤ a_i ≤ 10^9



Scoring

Subtask 1 [120 points]


* N = K

Subtask 2 [90 points]


* N ≤ 5
* a_i ≤ 7

Subtask 3 [140 points]


* There are no additional constraints.

Input Format


N K
a_1 a_2 a_3 ... a_N

Example

Input

5 5
3949 3774 3598 3469 3424


Output

1541
#include <bits/stdc++.h>

using namespace std;

int a[77];

int main() {
  int n, k;
  scanf("%d %d", &n, &k);
  for (int i = 0; i < n; ++i) {
    scanf("%d", a + i);
  }
  long long ans = 1e18;
  for (int i = 0; i < (1 << n); ++i) {
    int cnt = 0;
    for (int j = 0; j < n; ++j) {
      if ((i >> j) & 1) {
        ++cnt;
      }
    }
    if (cnt != k) {
      continue;
    }
    long long cur = 0;
    int mx = 0;
    for (int j = 0; j < n; ++j) {
      if ((i >> j) & 1) {
        if (a[j] <= mx) {
          cur += mx - a[j] + 1;
          ++mx;
        }
      }
      mx = max(mx, a[j]);
    }
    ans = min(ans, cur);
  }
  printf("%lld\n", ans);
}