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()))

money = 10**20

for i in range(2**n):
    cnt = 0
    b = a[:]
    max_b = b[0]
    for j in range(1, n):
        max_b = max(max_b, b[j])
        if i >> j & 1:
            cnt += max_b - b[j] + 1
            b[j] = max_b + 1
            max_b = b[j]
    col = 1
    m = b[0]
    for j in range(1, n):
        if b[j] > m:
            col += 1
            m = b[j]
    if col >= k:
        money = min(money, cnt)

print(money)