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;

namespace AtCoder
{
	class Program
	{
		static void Main(string[] args)
		{
			var firstLine = Console.ReadLine().Split(' ').Select(value => int.Parse(value)).ToList();
			var n = firstLine[0];
			var k = firstLine[1];

			var buildings = Console.ReadLine().Split(' ').Select(value => long.Parse(value)).ToList();

			var min = long.MaxValue;

			for(var bit = 0; bit < (1 << n); bit++)
			{
				var count = 0;
				for(var i = 0; i < n; i++)
				{
					if(((bit >> i) & 1) == 1)
					{
						count++;
					}
					else if(i == 0)
					{
						break;
					}
				}

				if(count != k)
				{
					continue;
				}

				long maxHeight = 0;
				long cost = 0;

				for(var i = 0; i < n; i++)
				{
					if(i == 0)
					{
						maxHeight = buildings[i];
						continue;
					}

					if(((bit >> i) & 1) == 1)
					{
						if(maxHeight >= buildings[i])
						{
							cost += maxHeight - buildings[i] + 1;
							maxHeight++;
						}
						else
						{
							maxHeight = buildings[i];
						}
					}
				}

				min = Math.Min(min, cost);
			}

			Console.WriteLine(min);
		}
	}
}