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
import java.util.*;
import java.lang.*;

class Main {

	public static void main(String[] args) throws Exception {
		final Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int k = sc.nextInt();
		int[] a = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = sc.nextInt();
		}

		long answer = Long.MAX_VALUE;
		for (int i = 0; i < (1 << n); i++) {
			if (Integer.bitCount(i) != k) continue;
			int ma = 0;
			long cost = 0;

			for (int j = 0; j < n; j++) {
				if (((i >> j) & 1) != 1) {
					ma = Math.max(ma, a[j]);
					continue;
				}

				if (ma < a[j]) {
					ma = a[j];
					continue;
				}

				cost += (ma - a[j]) + 1;
				ma++;
			}

			answer = Math.min(answer, cost);
		}

		System.out.println(answer);

	}
}
