Problem:
Score : 300 points

Problem Statement

In some other world, today is Christmas Eve.

There are N trees planted in Mr. Takaha's garden. The height of the i-th tree (1 \leq i \leq N) is h_i meters.

He decides to choose K trees from these trees and decorate them with electric lights. To make the scenery more beautiful, the heights of the decorated trees should be as close to each other as possible.

More specifically, let the height of the tallest decorated tree be h_{max} meters, and the height of the shortest decorated tree be h_{min} meters. The smaller the value h_{max} - h_{min} is, the better. What is the minimum possible value of h_{max} - h_{min}?

Constraints

2 \leq K < N \leq 10^5

1 \leq h_i \leq 10^9

h_i is an integer.

Input

Input is given from Standard Input in the following format:

N K
h_1
h_2
:
h_N

Output

Print the minimum possible value of h_{max} - h_{min}.

Sample Input 1

5 3
10
15
11
14
12

Sample Output 1

2

If we decorate the first, third and fifth trees, h_{max} = 12, h_{min} = 10 so h_{max} - h_{min} = 2. This is optimal.

Sample Input 2

5 3
5
7
5
7
7

Sample Output 2

0

If we decorate the second, fourth and fifth trees, h_{max} = 7, h_{min} = 7 so h_{max} - h_{min} = 0. This is optimal.

There are not too many trees in these sample inputs, but note that there can be at most one hundred thousand trees (we just can't put a sample with a hundred thousand lines here).

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

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

namespace AtCoder
{
    class Program
    {
        static void Main()
        {
            IO io = new IO();

            //ここから
            int n, k;
            int[] str = io.ReadLineToIntArray();
            n = str[0];
            k = str[1];
            int[] height = new int[n];
            for(int i = 0; i < n; i++)
            {
                height[i] = io.ReadLineToInt();
            }
            height = height.OrderBy(h => h).ToArray();

            int min = int.MaxValue;
            for(int i = 0; i < n - k+1; i++)
            {
                int temp = height[i + k - 1] - height[i];
                if (min > temp)
                {
                    min = temp;
                }
            }

            //ここまで
            Console.Write(min);
            Console.ReadKey();
        }
    }

    //関数
    public class Func
    {
        public void Swap<T>(ref T a,ref T b)
        {
            T temp;
            temp = a;
            a = b;
            b = temp;
        }
    }

    //IOを担う関数群
    public class IO
    {
        //stringの入力
        public string ReadLineToString()
        {
            return Console.ReadLine();
        }

        //intの入力
        public int ReadLineToInt()
        {
            return int.Parse(Console.ReadLine());
        }

        //空白区切りの複数の文字列の入力をstring[]にして返す
        public string[] ReadLineToStringArray()
        {
            return Console.ReadLine().Split(' ').ToArray();
        }


        //空白区切りの複数の整数の入力をint[]にして返す
        public int[] ReadLineToIntArray()
        {
            return Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
        }

        //空白区切りの複数の文字列の入力をList<string>で受け取る
        public List<string> ReadLineToStringList()
        {
            return Console.ReadLine().Split(' ').ToList();
        }

        //空白区切りの複数の整数の入力をList<int>で受け取る
        public List<int> ReadLineToIntList()
        {
            return Console.ReadLine().Split(' ').Select(int.Parse).ToList();
        }
    }

}