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
from itertools import product
n,k = (int(i) for i in input().split())
a = [int(i) for i in input().split()]
a2,ans = [0],float("inf")
for i in range(n): a2.append(max(a[i],a[-1]))
def g(q):
	c,f = 0,1
	if sum(q)<k-1: f = 0
	else:
		m = a[0]
		for i in range(n-1):
			if q[i]: m,c = max(a[i+1],m+1),c+max(m+1-a[i+1],0)
			elif m<a[i+1]:
				f = 0
				break
	if f: return c
	else: return float("inf")
for i in product((0,1),repeat=n-1): ans = min(ans,g(i))
print(ans)