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()))

ans = float('inf')
for bit in range(2**(N-1)):
    pre_num = a_list[0]
    ans_pre = 0
    count = 1
    index = []
    for i in  range(N-1):
        if bit & (1<<i):
            count+=1
            index.append(i+1)
            if pre_num >= a_list[i+1]:
                ans_pre += pre_num-a_list[i+1]+1
            
                pre_num += 1
                
            else:
                pre_num = a_list[i+1]
                
        else:
            pre_num = max(pre_num, a_list[i+1]+1)
    if count >= K:
        ans = min(ans, ans_pre)
            
print(ans)