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 = float("inf") 
for i in range(2**n):
    kar = a[:]
    b = format(i, 'b').rjust(n,"0")
    if b.count("1") != k:
        continue
    now = 0
    cou = 0
    for j in range(n):
        if b[j] == "1":
            cou += max(0,now - kar[j] + 1)
            kar[j] += max(0,now - kar[j] + 1)
        now = max(now,kar[j])
    ans = min(ans,cou)
print(ans)

        