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;
const int N = 16;
const long long inf = 1e15 + 15;
int n , k;
int arr[N];
long long solve(int pos , int len , int done){
	if(done >= k){
		return 0;
	}
	if(pos > n){
		return inf;
	}
	long long res = inf;
	res = min(res , solve(pos + 1 , max(len , arr[pos]) , done));
	int nlen = max(arr[pos] , len + 1);
	res = min(res , solve(pos + 1 , nlen , done + 1) + nlen - arr[pos]);
	return res;
}
int main(){
	scanf("%d %d" , &n , &k);
	for(int i = 1 ; i <= n ; ++i){
		scanf("%d" , arr + i);
	}
	printf("%lld\n" , solve(2 , arr[1] , 1));
}