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()))
# print(a)
ans = 10**15
for i in range(2**n):
    
    maxheight = a[0]
    money = 0
    see = 1
    for j in range(1,n):
        if see >= k:
            break 
        if a[j]>maxheight:
            see += 1
            maxheight = a[j]
        elif a[j]<=maxheight and (i>>j)&1 ==1:
            # print(i,j)
            money += maxheight-a[j]+1
            
            maxheight += 1
            see +=1
    # print(bin(i), money, maxheight,see)
    if see >= k and money <= ans:
        ans = money
print(ans)


