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;

int main() {
	long long N, K, A[15], count = 0, sum = 0, Max = 0, ans = pow(10, 18);
	cin >> N >> K;
	for (int i = 0; i < N; i++) {
		cin >> A[i];
	}
	for (long long i = 0; i < pow(2, N - 1); i++) {
		count = 1, Max = A[0], sum = 0;
		long long X = i;
		for (int j = 1; j < N; j++) {
			if (X % 2 == 1) {
				if (Max >= A[j]) {
					sum += Max - A[j] + 1;
					Max++;
				}
				else Max = A[j];
				count++;
			}
			else if (A[j] > Max) Max = A[j];
			X /= 2;
		}
		if (count >= K) ans = min(ans, sum);
	}
	cout << ans << endl;
}