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;

long long int N, K, b, i, r, m, n, a[20];
vector<bool> f;

int main(){
    scanf("%lld%lld", &N, &K);
    for(i = 0; i < N; ++i){
        scanf("%lld", a + i);
        f.push_back(i < K);
    }
    n = 1145141919810LL;
    do{
        r = 0;
        m = *a;
        for(i = 1; i < N; ++i){
            if(m >= a[i]){
                if(f[i]){
                    r += m - a[i] + 1;
                    ++m;
                }
            }else{
                m = a[i];
            }
        }
        n = min(r, n);
    }while(prev_permutation(f.begin(), f.end()));
    cout << n << endl;
    return 0;
}