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 <stdio.h>
#include <bits/stdc++.h>
using namespace std;
#define rep(i,n) for (int i = 0; i < (n); ++i)
#define Inf 1000000000000000000

int main(){
	
	int N,K;
	cin>>N>>K;
	
	vector<long long> a(N);
	rep(i,N)cin>>a[i];
	
	long long ans = Inf;
	rep(i,(1<<N)){
		vector<long long> b = a;
		int c = 0;
		long long maxi = 0;
		long long sum =0LL;
		rep(j,N){
			if((i>>j)&1){
				c++;
				if(maxi>=b[j]){
					sum += maxi+1-b[j];
					b[j] = maxi+1;
				}
				
			}
			maxi = max(maxi,b[j]);
		}
		if(c>=K)ans = min(ans,sum);
	}
	
	cout<<ans<<endl;
	
    return 0;
}

