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>
#include <algorithm>
 
#define rep(i, n) for(int i = 0; i < (n); ++i)
 
using namespace std;

typedef long long ll;

const ll inf = 1e11;

int n, k;
int a[15];

ll calc(int f){
    int s = 0;
    ll c = 0;
    rep(i, n){
        if(f >> i & 1 && a[i] <= s){
            ++s;
            c += s - a[i];
        }
        else{
            s = max(a[i], s);
        }
    }
    return c;
}

int main(){
    cin >> n >> k;
    rep(i, n){
        cin >> a[i];
    }

    ll ans = inf;
    rep(i, 1 << n){
        int c = 0;
        rep(j, n){
            c += i >> j & 1;
        }
        if(c >= k){
            ans = min(calc(i), ans);
        }
    }
    cout << ans << endl;
    return 0;
}