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()))
if K==1:
    print(0)
    exit()

ans = 10**12
for b in range(1<<(N-1)):
    h = A[0]
    k = 1
    cost = 0
    for i in range(N-1):
        a = A[i+1]
        if a > h:
            k += 1
            h = a
        elif b&(1<<i):
            k += 1
            cost += h+1 - a
            h += 1
    if k >= K:
        ans = min(ans, cost)
print(ans)