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>
#define int long long
using namespace std;
signed main(){
  int N,K;
  cin>>N>>K;
  vector<int> A(N);
  for(int &i:A)cin>>i;
  int ans=100000000000;
  for(int i=0;i<(1<<N);i++){
    if(__builtin_popcount(i)<K)continue;
    int cnt=0,mx=0;
    for(int j=0;j<N;j++){
      if(i>>j&1){
        if(mx>=A[j])mx++,cnt+=mx-A[j];
      }
      mx=max(mx,A[j]);
    }
    ans=min(ans,cnt);
  }
  cout<<ans<<endl;
}