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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class Main {
    private static Scanner sc;
    public static void main(String[] args) {
        Main instance = new Main();
        sc = instance.new Scanner();
        instance.solve();
    }

    private void solve() {
        try {
            int N = sc.nextInt();
            int K = sc.nextInt();
            int[] h = new int[N];
            for (int i = 0; i < N; i++) {
                h[i] = sc.nextInt();
            }

            Arrays.sort(h);
            int min = Integer.MAX_VALUE;
            int tmp;
            for (int i = 0; i < N - K + 1; i++) {
                tmp = h[i+K-1] - h[i];
                if (min > tmp ) min = tmp;
            }
            System.out.println(min);


        } catch (Exception e) {
            e.printStackTrace();
        }
    }

    private int gcd(int a, int b) {
        if (a < b) return gcd(b, a);
        if (b == 0) return a;
        return gcd(b, a%b);
    }

    private int gcd(int[] param) {
        final int len = param.length;
        int g = gcd(param[0], param[1]);
        for (int i = 1; i < len - 1; i++) {
            g = gcd(g, param[i+1]);
        }
        return g;
    }

    private class Scanner {
        String[] s;
        int i;
        BufferedReader br;
        String regex = " ";

        public Scanner() {
            s = new String[0];
            i = 0;
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        @Override
        protected void finalize() throws Throwable {
            try {
                super.finalize();
            } finally {
                destruction();
            }
        }

        private void destruction() throws IOException {
            if (br != null) br.close();
        }

        public String next() throws IOException {
            if (i < s.length) return s[i++];
            String st = br.readLine();
            while (st == "") st = br.readLine();
            s = st.split(regex, 0);
            i = 0;
            return s[i++];
        }

        public int nextInt() throws NumberFormatException, IOException {
            return Integer.parseInt(next());
        }

        public Long nextLong() throws NumberFormatException, IOException {
            return Long.parseLong(next());
        }

        public Double nextDouble() throws NumberFormatException, IOException {
            return Double.parseDouble(next());
        }
    }
}