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 <vector>
using namespace std;

int main() {
	int N, K; cin >> N >> K;
	vector<long> a(N);
	for(int i=0; i<N; ++i) cin >> a[i];
	long ans=1e15;
	for(int bit=1; !(bit&(1<<N)); bit += 2){
	    long h=0, now=0;
	    int cnt=0;
	    for(int i=0; i<N; ++i){
	        if(bit&(1<<i)){
	            if(h<a[i]) h=a[i];
	            else{
	                now += h+1-a[i];
	                ++h;
	            }
	            ++cnt;
	        }
	        else h=max(h, a[i]);
	    }
	    if(cnt>=K) ans=min(ans, now);
	}
	cout << ans << endl;
	return 0;
}
