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
def LI(): return list(map(int,input().split()))
N,K = LI()
a = LI()
ans = float('INF')
for i in range(2**(N-1)):
    bit = [i>>j&1 for j in range(N-1)]
    if K-1!=sum(bit):
        continue
    cost,kijun = 0,a[0]
    for k in range(N-1):
        if bit[k]==0:
            kijun = max(kijun,a[k+1])
            continue
        if a[k+1]>=kijun+1:
            kijun = a[k+1]
            continue
        cost += (kijun+1)-a[k+1]
        kijun += 1
    ans = min(ans,cost)
print(ans)