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 = [int(x) for x in input().split()]
_min = 1145141919810
for i in range(2**(n-1)):
    ctr = 0
    val = 0
    h_max = a[0]
    for j in range(n-1):
        if (i>>j)&1:
            ctr+=1
            h_max = h_max+1 if h_max>=a[j+1] else a[j+1]
            val+=h_max-a[j+1]
        if h_max<a[j+1]:
            h_max = a[j+1]
    if ctr==k-1 and val<_min:
        _min = val
print(_min)