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 = list(map(int,input().split()))
A = list(map(int,input().split()))
MIN = float('inf')
for bit in range(1<<N):
    tmpA = A[:]
    L = []
    for i in range(N):
        if bit & (1<<i):
            L.append(i)
    SUM = 0
    for l in L:
        MAX = max(tmpA[:l]+[0])
        if MAX >= tmpA[l]:
            SUM += MAX+1-tmpA[l]
            tmpA[l] = MAX+1
    count = 0
    MAX = 0
    for i in range(N):
        if tmpA[i] > MAX:
            count += 1
            MAX = tmpA[i]
    if count >= K:
        MIN = min(MIN,SUM)
print(MIN)