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;

template <typename T>
bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int N, K;
  cin >> N >> K;
  vector<int> A(N);
  for (int i = 0; i < N; i++) {
    cin >> A[i];
  }
  int64_t res = 1LL << 60;
  for (int bit = 0; bit < (1 << N); bit++) {
    int64_t cost = 0;
    int k = 1, ma = A[0];
    for (int i = 1; i < N; i++) {
      int diff = 0;
      if ((bit >> i) & 1) {
        diff = max(0, ma - A[i] + 1);
        cost += diff;
      }
      if (chmax(ma, A[i] + diff)) k++;
    }
    if (k >= K) res = min(res, cost);
  }
  cout << res << '\n';
  return 0;
}
