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: Wrong Answer)

# https://atcoder.jp/contests/s8pc-4/tasks/s8pc_4_b

n, k = map(int, input().split())
buildings = list(map(int, input().split()))
# 一番目は必ず見えるとして、それ以外のどれが見えるかを考える。
# どれが見えるかは、全部やればいい。
most_left = buildings[0]
buildings = buildings[1:]
ans = float('inf')
for i in range(2 ** len(buildings)):
    if bin(i).count('1') != k - 1:
        continue
    t = most_left
    cost = 0
    for j in range(len(buildings)):
        if (i >> j) & 1:
            if t > buildings[j]:
                cost += t - buildings[j] + 1
                t += 1
    ans = min(ans, cost)
print(ans)