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>
#define rep(i,n)for(int i=0;i<(n);i++)
using namespace std;
typedef long long ll;

ll a[15];
int main() {
	ll n, k; scanf("%lld%lld", &n, &k);
	rep(i, n)scanf("%lld", &a[i]);
	ll Min = LLONG_MAX;
	rep(i, 1 << n) {
		ll Max = -1;
		ll sum = 0;
		int cnt = 0;
		rep(j, n) {
			if (!(i >> j & 1)) {
				Max = max(Max, a[j]); continue;
			}
			cnt++;
			if (Max >= a[j]) {
				sum += Max + 1 - a[j];
				Max = Max + 1;
			}
			Max = max(Max, a[j]);
		}
		if (cnt < k)continue;
		Min = min(Min, sum);
	}
	cout << Min << endl;
}