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;
#define all(x) (x).begin(),(x).end()
const int mod=1000000007,MAX=103;
const ll INF=1LL<<60;

int main(){
    
    int N,K;cin>>N>>K;
    vector<ll> S(N),T(N);
    for(int i=0;i<N;i++){
        cin>>S[i];
        if(i<K) T[i]=1;
        else T[i]=0;
    }
    
    sort(all(T));
    
    ll ans=INF;
    
    do{
        ll sum=0;
        ll M=0;
        for(int i=0;i<N;i++){
            if(T[i]){
                if(S[i]>M){
                    M=S[i];
                }else{
                    sum+=(M+1-S[i]);
                    M++;
                }
            }else M=max(M,S[i]);
        }
        //cout<<sum<<endl;
        ans=min(ans,sum);
    }while(next_permutation(all(T)));
    
    cout<<ans<<endl;
}

