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<bits/stdc++.h>
using namespace std;
typedef long long ll;
ll n,k,a[15],L,ans,cnt,MIN=1e18;
int main(void){
    cin>>n>>k;
    for(int i=0;i<n;i++){
        cin>>a[i];
    }
    for(int i=0;i<(1<<(n-1));i++){
        L=a[0];
        cnt=0;
        ans=0;
        for(int j=1;j<n;j++){
            if((i>>(j-1))&1){
                cnt++;
                if(L>=a[j]){
                    ans+=L-a[j]+1;
                    L++;
                }
            }
            L=max(L,a[j]);
        }
        if(cnt+1>=k){
            MIN=min(ans,MIN);
        }
    }
    cout<<MIN<<endl;
}
