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
from itertools import combinations as comb

N, K = map(int, input().split())
a = list(map(int, input().split()))
ans = 10**17

for i in comb([n for n in range(1, N)], K-1):
    tmpa = a[:]
    tmp = 0
    for j in range(K-1):
        pre = max(tmpa[:i[j]])
        if tmpa[i[j]] <= pre:
            tmp += pre+1-tmpa[i[j]]
            tmpa[i[j]] = pre+1
    
    if tmp < ans:
        ans = tmp

print(ans)