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()))

candidate = [[0], [1]]
while True:
    temp = []
    for c in candidate:
        temp.append(c + [0])
        temp.append(c + [1])
    candidate = temp
    if len(temp[0]) == N:
        break

ans = float('inf')
for c in candidate:
    if sum(c) != K:
        continue
    high = a[0]
    temp = 0
    for i, value in enumerate(c):
        if i == 0:
            continue
        if value == 1 and a[i] <= high:
            high += 1
            temp += high - a[i]
        high = max(high, a[i])


    ans = min(ans, temp)

print(ans)