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
n, k = map(int, input().split())
A = list(map(int, input().split()))

# 見る建物を決め打ち、コストを計算して最小値が答え。
# 左端は見えてしまうので、それを除いたn-1個からk-1個を選ぶ

from itertools import combinations

ptn = combinations(range(1, n), k - 1)

ans = 10 ** 19
for p in ptn:
  totalcost = 0
  repA = A[:]
  for itr, val in enumerate(p):
    cost = max(0, max(repA[:val]) + 1 - repA[val])
    repA[val] += cost
    totalcost += cost
  ans = min(ans, totalcost)
print(ans)