Problem:
Max Score: 350 Points

Problem Statement

There are N buildings along the line. The i-th building from the left is colored in color i, and its height is currently a_i meters.

Chokudai is a mayor of the city, and he loves colorful thigs. And now he wants to see at least K buildings from the left.

You can increase height of buildings, but it costs 1 yens to increase 1 meters. It means you cannot make building that height is not integer.

You cannot decrease height of buildings.

Calculate the minimum cost of satisfying Chokudai's objective.

Note: "Building i can see from the left" means there are no j exists that (height of building j) ≥ (height of building i) and j < i.

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.

Sample Input 1

5 5
3949 3774 3598 3469 3424

Sample Output 1

1541

The optimal solution is (height of buildings from the left) = [3949, 3950, 3951, 3952, 3953].

Sample Input 2

5 3
7 4 2 6 4

Sample Output 2

7

The optimal solution is (height of buildings from the left) = [7, 8, 2, 9, 4].

Solution in PyPy3 (2.4.0) (judge verdict: Accepted)

from itertools import product

inf = 10 ** 19

def main():
    n, k = map(int, input().split())
    num_list = list(map(int, input().split()))

    ans = inf

    for bit in list(product([0, 1], repeat = n)):
        count = bit.count(1)
        if count < k:
            continue
        tmp = 0
        max_hight = 0
        for i in range(n):
            if bit[i] != 1:
                max_hight = max(max_hight, num_list[i])
                continue
            if max_hight >= num_list[i]:
                tmp += max_hight - num_list[i] + 1
                max_hight += 1
            else:
                max_hight = num_list[i]
        ans = min(ans, tmp)
    
    print(ans)

if __name__ == '__main__':
    main()