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 = list(map(int, input().split(" ")))
a = list(map(int, input().split(" ")))

ans = max(a) * N

for i in range(pow(2, N)):
    candidate = bin(i)[2:].zfill(N)
    if candidate.count("1") != K:
        continue

    cost = 0
    local_min = a[0] - 1
    for j, build in enumerate(a):
        if candidate[j] == "1":
            cost += max(0, local_min + 1 - build)
            local_min = max(build, local_min + 1)
        else:
            local_min = max(build, local_min)

    ans = min(ans, cost)

print(ans)
