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

#左からi個、k種類選んだ場合
#dp[i][k]=cost



result=10**100
for i in range(2**(n-1)):
    #print(bin(i))
    if str(bin(i)).count("1")>=k-1:
        #print(">>>>>>",bin(i))
        bk=a[0]
        cost=0
        for j in range(n-1):
            if i>>j&1:
                if bk<a[j+1]:
                    bk=a[j+1]
                else:
                    bk+=1
                    cost+=(bk-a[j+1])
            else:
                bk=max(bk,a[j+1])
                #print(bk,a[j+1],bk-a[j+1])
        result=min(cost,result)
print(result)

