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
import java.util.*;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int k = sc.nextInt();
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = sc.nextInt();
        }
        Long ans = Long.MAX_VALUE;
        for (int i = 0; i < 1<<n; i++) {
            if(Integer.bitCount(i) < k)continue;
            long t = 0L;
            int preh = -1;
            for (int j = 0; j < n; j++) {
                if((i>>j & 1) != 1){
                    if(preh < a[j]) preh = a[j];
                    continue;
                }
                if(a[j] < preh+1) t += preh+1-a[j];
                preh = Math.max(a[j], preh+1);
            }
            if(t < ans) ans = t;
        }
        System.out.println(ans);
        sc.close();

    }

}
