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
import itertools

n, k = map(int, input().split())
a = list(map(int, input().split()))
b = []
max_h = 0
for i, num in enumerate(a):
    b.append(max_h)
    max_h = max(max_h, num)

ans = 9999999999999999999999
for lst in itertools.combinations(range(1, n), k - 1):
    total = 0
    before = a[0]
    for num in lst:
        if a[num] <= b[num] or a[num] <= before:
            total += max(b[num], before) - a[num] + 1
            before = max(b[num], before) + 1
            
    ans = min(ans, total)
print(ans)