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: Wrong Answer)

using System;
using System.IO;

class Program
{
    static void Main()
    {
        string[] Input = Console.ReadLine().Split(' ');
        int N = int.Parse(Input[0]);
        int K = int.Parse(Input[1]);
        long[] h = new long[N];
        long[] H = new long[N];
        long[] tmp = new long[N];

        long[,] Baketu = new long[10, N];
        long[] BaketuNumber = new long[10];   //0~9まで保存する
        

        for (int i = 0; i < N; i++)
        {
            h[i] = long.Parse(Console.ReadLine());
            H[i] = 0;
            tmp[i] = h[i];
        }

        //入力完了

        //とりあえずBaketuNumberを全部0にする
        //その後10回基数ソートする

        for (int i = 0; i < 10; i++)
        {
            BaketuNumber[i] = 0;
        }

        for (int i = 0; i < 10; i++)
        {
//            Console.WriteLine("\n");
//            long cnt = 0;

            for (int j = 0; j < N; j++)
            {
                tmp[j] = h[j];
                for (int k = 0; k < i; k++)
                {
                    tmp[j] /= 10;
                }
//                Console.WriteLine("{0} {1}", tmp[j], i);
                //まずバケツナンバーに1の位の数を入れる
                //バケツナンバー、バケツに入っている要素数
                BaketuNumber[tmp[j] % 10]++;
                //バケツナンバー、バケツのそのままの値
                Baketu[tmp[j] % 10, BaketuNumber[tmp[j] % 10] - 1] = h[j];

//                cnt++;
                //ここでtmp[j] % 10がひとけた上の数字をとれるようにする
            }

            int cnt2 = 0;
            int cnt3 = 0;

            for (int j = 0; j < N; j++)
            {

                bool check = false;
                do
                {
                    //でそれから新しいHにそれを入れる
                    if (BaketuNumber[cnt2] > 0) //もしn(0~9)番目のバケツに入ってたら
                    {
                        //まずh[j]に入れる
                        h[j] = Baketu[cnt2, cnt3];
                        Baketu[cnt2, cnt3] = 0;
                        cnt3++;

                        BaketuNumber[cnt2]--;

                        check = true;
                    }
                    else
                    {
                        cnt2++;
                        cnt3 = 0;
                    }
                } while (check == false);
                
            }
        }

        for (int i = 0; i < N; i++)
        {
            Console.WriteLine(h[i]);
        }

        //iが小さい順にでかい木

        long hMin = 1000000000;

        for (int i = 0; i < N - (K - 1); i++)
        {
            if (h[i + (K - 1)] - h[i] < hMin)
            {
                hMin = h[i + (K - 1)] - h[i];
            }
        }

        Console.WriteLine(hMin);
    }
}