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 itertools

N, K = map(int, input().split())
A = list(map(int, input().split()))

ans = 10**11
for obj in itertools.combinations(range(1,N), K-1):
	tmp = A[0]
	cnt = 1
	i = 0
	cost = 0
	for j in range(1,N):
		if j == obj[i]:
			cost += max(0, tmp-A[j]+1)
			tmp = max(tmp+1, A[j])
			i += 1
			cnt += 1
			if cnt == K:
				break
		
		else:
			if A[j] > tmp:
				cnt += 1
				tmp = A[j]

			if cnt == K:
				break

	ans = min(ans, cost)

print(ans)