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;
typedef long long ll;
const ll MOD = 1e9+7;
int main() {
    ll n,k;
    cin >> n >> k;
    vector<ll>a(n);
    for(ll i=0;i<n;i++){
        cin >> a[i];
    }
    ll ans=1e15;
    for(ll i=0;i<(1<<n);i++){
        ll cost=0;
        ll mh=0;
        ll num=0;
        vector<ll>b=a;
        for(ll j=0;j<n;j++){
            if(i & (1<<j)){
                cost+=max((ll)0,mh+1-b[j]);
                b[j]=max(b[j],mh+1);
                if(b[j]>mh) num++;
            }
            mh=max(mh,b[j]);
        }
        if(num>=k) ans=min(ans,cost);
    }
    cout << ans << endl;
}