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>
#include<unordered_set>
#include<unordered_map>
using namespace std;

int n;
int k;

vector<long long int> v;

int cn(int num){
	int r = 0;
	while (num){
		if ((num & 1)){
			r++;
		}
		num >>= 1;
	}
	return r;
}
int main(){
	cin >> n >> k;
	for (int i = 0; i < n; i++){
		int a;
		scanf("%d", &a);
		v.push_back(a);
	}
	long long int ans = LLONG_MAX;
	for (int i = 0; i < (1 << n); i++){
		int val = cn(i);
		if (val != k)continue;
		long long int mx = LLONG_MIN;
		long long int cost = 0;
		for (int j = 0; j < n; j++){
			if ((i >> j) & 1){
				if(mx>=v[j])cost += max(0LL, mx + 1LL - v[j]);
				mx++;
			}
			mx = max(mx, v[j]);
		}
		ans = min(ans, cost);
	}
	printf("%lld\n", ans);
	return 0;
}