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()))

ans = 10**11
for i in range(2**n):
    temp = 0
    b = a[:]
    i = format(i, "0{}b".format(n))
    if i.count("1") == k:
        maxi = 0
        for j in range(n):
            if i[j] == "1":
                if maxi >= b[j]:
                    temp += maxi - b[j] + 1
                    b[j] = maxi + 1
            maxi = max(maxi, b[j])
        ans = min(ans, temp)


print(ans)
