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

ans=float('inf')
for i in range(2**N):
    b=copy.deepcopy(a)
    num=0
    for j in range(N):
        if i>>j&1:
            num+=max(b[:j+1])+1-b[j]
            b[j]=max(b[:j+1])+1
    o=1
    #print(b)
    for y in range(1,N):
        if max(b[:y])<b[y]:
            o+=1
    if o>=K:
        
        ans=min(num,ans)
        #print(ans,b)
print(ans)