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.Collections.Generic;
using System.Linq;
using System.Text;
//using System.Threading.Tasks;

namespace B
{
    class Program
    {
        class Build
        {
            int num;
            int data; //高さ
        }

        static void Main(string[] args)
        {
            long[] NK = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
            long[] inp = Console.ReadLine().Split(' ').Select(y => long.Parse(y)).ToArray();
            long[] input = new long[inp.Length + 1];
            input[inp.Length] = -1;
            for (int i = 0; i < inp.Length; ++i) input[i] = inp[i];

            long[] top = new long[NK[1]]; //高い順
            top[0] = 0; //インデックス
            //高いのをsearch
            for(int i = 1; i < top.Length; ++i)
            {
                long max = inp.Length;
                for(int j = 1; j < input.Length; ++j)
                {
                    if((input[max] < input[j])&&(Array.IndexOf(top,j) < 0)){
                        max = j;
                    }
                }
                top[i] = max;
            }
            long ans = 0;
            Array.Sort(top);
            //foreach (var i in top) Console.WriteLine(i);
            for(int i = 1; i < top.Length; ++i)
            {
                //Console.WriteLine(input[0] +" > "+input[top[i]]);
                //前 > 後

                if (input[top[i-1]] >= input[top[i]])
                {
                    ans += input[top[i - 1]] - input[top[i]] + 1;
                    input[top[i]] = input[top[i-1]] + 1;
                }
                else
                {
                    if(input[top[i-1]] > input[top[i]])
                    {
                        ans += input[top[i - 1]] - input[top[i]] + 1;
                        input[top[i]] = input[top[i - 1]] + 1;
                    }
                    else
                    {

                    }
                }
            }
            Console.WriteLine(ans);
        }
    }
}