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;

typedef long long int64;

const int64 INF = 1LL << 58;

int main()
{
  int64 N, K, A[15];

  cin >> N >> K;
  for(int i = 0; i < N; i++) {
    cin >> A[i];
  }

  int64 ret = INF;
  for(int i = 0; i < 1 << N; i++) {
    if(__builtin_popcount(i) < K) continue;
    int64 cost = 0, last = 0;
    for(int j = 0; j < N; j++) {
      if((i >> j) & 1) {
        last = max(last + 1, A[j]);
        cost += last - A[j];
      } else if(A[j] > last) {
        cost = INF;
      }
    }
    ret = min(ret, cost);
  }

  cout << ret << endl;
}

