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
# https://atcoder.jp/contests/s8pc-4/tasks/s8pc_4_b

from itertools import combinations

N,K=map(int,input().split())
a=list(map(int,input().split()))

minc=10**12
ai=[i for i in range(N)]
for i in combinations(ai,K):
    ac=a[:]
    cost=0
    i=list(i)
    for j in range(1,K):
        costt=max(max(ac[:i[j]])-ac[i[j]]+1,0)
        ac[i[j]]+=costt
        cost+=costt
    minc=min(cost,minc)
print(minc)