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(2 ** (N-1)):
    l = [0] * (N-1)
    for j in range(N-1):
        if (i >> j) & 1:
            l[j] = 1
    cost = 0
    AA = A.copy()
    for k in range(N-1):
        if l[k] == 1:
            maxA = max(AA[:k+1])
            if maxA >= AA[k+1]:
                diff = maxA - AA[k+1] + 1
                AA[k+1] = maxA + 1
                cost += diff
    cnt = 1
    for num in range(1, N):
        if AA[num] > max(AA[:num]):
            cnt += 1
    if cnt >= K:
        ans = min(ans, cost)
print(ans)