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 N == 1:
    cost = 0
else:
    cost = 10 ** 11

for i in range(2 ** (N - 1)):
    r = str(format(i, 'b')).zfill(N - 1)
    ma = a[0]
    k = 1
    p = 0
    for j in range(N - 1):
        if r[j] == '1':
            k += 1
            if a[1 + j] > ma:
                ma = a[1 + j]
            elif a[1 + j] <= ma:
                p += ma - a[1 + j] + 1
                ma = ma + 1
        elif r[j] == '0':
            if a[1 + j] > ma:
                ma = a[1 + j]
    if k >= K and p < cost:
        cost = p

print(cost)