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()))
L = [_ for _ in range(1,N)]
ans = float("inf")
cand = list(itertools.combinations(L,K-1))
#print(cand)
for C in cand:
  C = list(C)
  C.sort()
  temp = 0
  prev = A[0] #最初のビルは必ず見える。
  #print(C)
  Flag = True
  for i in C:
    #print(prev,min(A[:i]))
    if prev < max(A[:i]):
      #print(C)
      Flag = False
      break
    if A[i] <= prev:
      prev += 1
      temp += prev-A[i]
    else:
      prev = A[i]
  if Flag:
    ans = min(ans,temp)
print(ans)