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)
buildings = gets.chomp.split.map(&:to_i)

def main(n, k, buildings)
  min = Float::INFINITY
  (0..2**n-1).each do |n_ten|
    n_two = n_ten.to_s(2).rjust(n, '0')
    extending = n_two.chars.map(&:to_i)
    next if extending.count { |flag| flag == 1 } < k

    amount = 0

    dupped_buildings = buildings.dup
    current_max = 0
    dupped_buildings.each.with_index do |building, index| 
      if index == 0
        current_max = [building, current_max].max
        next building 
      end

      if extending[index] == 0
        current_max = [building, current_max].max
        next building 
      end

      if current_max < dupped_buildings[index]
        current_max = [dupped_buildings[index], current_max].max
        next dupped_buildings[index]
      else
        diff = (current_max - dupped_buildings[index]) + 1
        dupped_buildings[index] += diff
        amount += diff
        current_max = [dupped_buildings[index], current_max].max
        next dupped_buildings[index]
      end
    end

    
    amount = amount

    if amount < min
      min = amount 
    end
  end
  min 
end

puts main(n, k, buildings)