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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Linq;
using System.Collections.Generic;
using System.Text;

class P
{
    static void Main(string[] _)
    {

        _ = Console.ReadLine().Split(' ');
        int n = int.Parse(_[0]);
        int k = int.Parse(_[1]);
        _ = Console.ReadLine().Split(' ');
        int[] a = new int[n];
        int first = 0;
        for (int i = 0; i < n; i++)
        {
            a[i] = int.Parse(_[i]);
            if (i == 0)
            {
                first = a[i];
            }
            a[i] -= first;
        }
        int cost = 0;
        
        for (int i = 1; i < k; i++)
        {
            if (a[i-1] >= a[i])
            {
                int tmp = a[i-1] - a[i] + (a[i - 1] == a[i] ? 1 : 0);
                cost += tmp;
                a[i] += tmp;
            }
        }
        Console.WriteLine(cost);
    }
}