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 combinations
N,K = map(int,input().split())
A = list(map(int,input().split()))
cmin = 10**12
for x in combinations(range(1,N),K-1):
    C = A[:]
    B = [0]
    B += x
    B = sorted(B)
    cnt = 0
    for i in range(1,K):
        j0 = B[i-1]
        j1 = B[i]
        h = 0
        for j in range(j0,j1):
            h = max(h,C[j])
        if C[j1]<=h:
            cnt += h+1-C[j1]
            C[j1] = h+1
    cmin = min(cmin,cnt)
print(cmin)