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 = list(map(int,input().split()))

# 建物iをミられる高さにするかいなかのbit探索

ans = 100010001000100010001000

for byte in range(pow(2,N-1)):
    height = a_list[0]
    cost = 0
    if bin(byte).count("1")>=K-1:
        for i in range(N-1):
            if not (byte & 1<<i)==0: # i番目を見る場合
                cost += max(0, height + 1 - a_list[i+1])
                height = max(height + 1, a_list[i+1])
            else:
                height = max(height,a_list[i+1])
        ans = min(ans,cost)
print(ans)