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 = [int(i) for i in input().split()]
A = [int(i) for i in input().split()]
ans = float('inf')

for i in range(2**N):
    cnt = 0
    last = 0
    cost = 0
    for j in range(N):
        if(A[j] > last):
            cnt += 1
            last = A[j]
        elif(i>>j & 1):
            cnt += 1
            cost += last-A[j]+1
            last += 1
    if(cnt>=K):
        ans = min(ans, cost)
print(ans)