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
cin = open(0).read().strip().split('\n')
n, k = map(int, cin[0].split(' '))
a = list(map(int, cin[1].split(' ')))

ret = float('inf')
for idx in range(2**(n)):
    colors = 0
    res = 0
    left = 0
    for i in range(n):
        if (idx>>i) & 1:
            colors += 1
            res += max(left+1 - a[i] , 0)
            left = max(a[i], left+1)
        else:
            colors += 1 if left < a[i] else 0
            left = max(left, a[i])


    if colors >= k:
        ret = min(ret, res)

print(ret)