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].