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 <iostream>
#include <cmath>

using namespace std;

int main(){
    int N, K;
    cin >> N >> K;

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

    long ans = 10000000000000;
    for(int i=0; i<pow(2,N); i++){
        int max = a[0];
        long t = 0;
        int cnt = 1;
        for(int j=1; j<N; j++){
            if(a[j] > max){
                cnt++;
                max = a[j];
                continue;
            }
            if((i >> j) & 1){
                t += max - a[j] + 1;     
                max = max + 1;
                cnt++;
            }
        }
        if(cnt <K) continue;
        if(t <= ans) ans = t;
    }

    cout << ans << endl;

    return 0;
}