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 Ruby (2.7.1) (judge verdict: Accepted)

N,K = gets.chomp.split.map(&:to_i)
a = gets.chomp.split.map(&:to_i)

if K == 1
  p 0
  exit
end

ans = 10**15
[0,1].repeated_permutation(N-1) do |arr|
  next if arr.sum < K-1

  h = a.first
  sum = 0

  1.upto(N-1) do |i|
    if arr[i-1] == 1 # 見える
      if a[i] > h
        h = a[i]
      else
        sum += (h+1 - a[i])
        h += 1
      end
    else
      h = [h,a[i]].max
    end
  end

  ans = [ans,sum].min
end
p ans