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()))
ans = float("inf")
for i in range(1,2**n):
    l = [j for j in range(n) if i>>j&1]
    if l[0] != 0 or len(l) != k:
        continue
    m = 0
    s = 0
    for j in range(n):
        if (j in l) and (a[j] <= m):
            s += m+1-a[j]
            m += 1
        m = max(m,a[j])
    #print(l,s)
    ans = min(ans,s)

print(ans)