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 (2.3.3) (judge verdict: Accepted)

n, k = gets.split().map(&:to_i)
a = gets.split().map(&:to_i)

len = n - 1
target = k - 1
cost = 10000000000000

[0, 1].repeated_permutation(len) do |bits|
  next unless bits.count(1) == target
  baseH = a[0]
  sum = 0
  bits.each_with_index do |bit, index|
    next if bit == 0
    baseH = [a[0..index].max, baseH].max
    if baseH < a[index+1]
      baseH = a[index+1]
    else
      sum += baseH - a[index+1] + 1
      baseH += 1
    end
  end
  cost = [cost, sum].min
end

puts cost