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 <vector>
using namespace std;

int main(){
    int n, k;
    cin >> n >> k;
    vector<int> a(n);
    for(int i = 0; i < n; i++) cin >> a[i];

    long long int ans = 1001001001001;
    for(int bit = 0; bit < (1 << n); bit++){
        long long int coans = 0;
        int colornum = 0;
        int height = 0;
        for(int i = 0; i < n; i++){
            if(bit & (1 << i)){
                colornum++;
                if(a[i] > height){
                    height = a[i];
                }else{
                    coans += height-a[i]+1;
                    height++;
                }
            }else{
                if(height < a[i]) height = a[i];
            }
        }
        
        if(colornum >= k && coans < ans) ans = coans;
    }
    cout << ans << endl;
    return 0;
}