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.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.AbstractMap;
import java.util.Arrays;
import java.util.NoSuchElementException;

/** C */
public class Main {
	public static void main(String[] args) {
		FastScanner sc = new FastScanner();
		int N = sc.nextInt();
		int K =  sc.nextInt();

		int[] ary = new int[N];
		for(int i = 0; i < N; i++) {
			ary[i] = sc.nextInt();
		}

		Arrays.sort(ary);
//
//		int[] ruiseki = new int[N+1];
//		for(int i = 0; i < N; i++) {
//			ruiseki[i+1] = ary[i] + ruiseki[i];
//		}

	    int ans = ary[N-1] - ary[0];
	    int tmp = 99999999;
	    for (int i=0; i < N-K+1; i++) {
	        tmp = ary[i+K-1] - ary[i];
	        if (ans > tmp) {
	            ans = tmp;
	        }
	    }



		//************************************/
		// ここから出力処理
		//************************************/
		PrintWriter out = new PrintWriter(System.out);


		out.println(ans);

		// 最後に必ずFlush
		out.flush();
	}
}


///** ABC115-A */
//public class Main {
//	public static void main(String[] args) {
//		FastScanner sc = new FastScanner();
//		int N = sc.nextInt();
//
//
//		//************************************/
//		// ここから出力処理
//		//************************************/
//		PrintWriter out = new PrintWriter(System.out);
//
//
//		if(N == 25){
//			out.println("Christmas");
//
//		}else if(N == 24) {
//			out.println("Christmas Eve");
//
//		}else if(N == 23) {
//			out.println("Christmas Eve Eve");
//
//		}else if(N == 22) {
//			out.println("Christmas Eve Eve Eve");
//
//		}
//
//		// 最後に必ずFlush
//		out.flush();
//	}
//}

//
/////** B */
//public class Main {
//	public static void main(String[] args) {
//		FastScanner sc = new FastScanner();
//		int N = sc.nextInt();
//		int[] ary = new int[N];
//		int sum = 0;
//
//		for(int i = 0; i < N; i++) {
//			ary[i] = sc.nextInt();
//			sum += ary[i];
//		}
//
//		Arrays.sort(ary);
//
//		sum -= (ary[N-1] /2);
//
//
//		//************************************/
//		// ここから出力処理
//		//************************************/
//		PrintWriter out = new PrintWriter(System.out);
//
//
//		out.println(sum);
//
//		// 最後に必ずFlush
//		out.flush();
//	}
//}





///** テンプレート */
//public class Main {
//	public static void main(String[] args) {
//		FastScanner sc = new FastScanner();
//		int N = sc.nextInt();
//		int M =  sc.nextInt();
//
//		int[] ary = new int[N];
//		for(int i = 0; i < N; i++) {
//			ary[i] = sc.nextInt();
//		}
//
//		//************************************/
//		// ここから出力処理
//		//************************************/
//		PrintWriter out = new PrintWriter(System.out);
//
//
//		out.println("hoge");
//
//		// 最後に必ずFlush
//		out.flush();
//	}
//}

/** スキャン用 */
class FastScanner {
	private final InputStream in = System.in;
	private final byte[] buffer = new byte[1024];
	private int ptr = 0;
	private int buflen = 0;

	/** クラス内部用だよ */
	private boolean hasNextByte() {
		if (ptr < buflen) {
			return true;
		} else {
			ptr = 0;
			try {
				buflen = in.read(buffer);
			} catch (IOException e) {
				e.printStackTrace();
			}
			if (buflen <= 0) {
				return false;
			}
		}
		return true;
	}

	/** クラス内部用だよ */
	private int readByte() {
		if (hasNextByte()) {
			return buffer[ptr++];
		} else {
			return -1;
		}
	}

	/**
	 * クラス内部用だよ
	 * ASCII の文字の内、表示用の文字を返す関数
	 *
	 * @return 改行とか制御文字じゃない、表示用文字ならtrue
	 * */
	private static boolean isPrintableChar(int c) {
		return 33 <= c && c <= 126;
	}

	/**
	 * @return 改行文字とか空白以外を除いた、次の文字があればtrue
	 * */
	public boolean hasNext() {
		while (hasNextByte() && !isPrintableChar(buffer[ptr])) {
			ptr++;
		}
		return hasNextByte();
	}

	/**
	 *
	 * @return 次の文字列
	 */
	public String next() {
		if (!hasNext()) {
			throw new NoSuchElementException();
		}

		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while (isPrintableChar(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	/**
	 *
	 * @return 次のLong
	 */
	public long nextLong() {
		if (!hasNext())
			throw new NoSuchElementException();
		long n = 0;
		boolean minus = false;
		int b = readByte();
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		if (b < '0' || '9' < b) {
			throw new NumberFormatException();
		}
		while (true) {
			if ('0' <= b && b <= '9') {
				n *= 10;
				n += b - '0';
			} else if (b == -1 || !isPrintableChar(b)) {
				return minus ? -n : n;
			} else {
				throw new NumberFormatException();
			}
			b = readByte();
		}
	}

	/**
	 *
	 * @return 次のInt
	 */
	public int nextInt() {
		long nl = nextLong();
		if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE)
			throw new NumberFormatException();
		return (int) nl;
	}

	/**
	 *
	 * @return 次のDouble
	 */
	public double nextDouble() {
		return Double.parseDouble(next());
	}
}

class Pair<K, V> extends AbstractMap.SimpleEntry<K, V> {
	/** serialVersionUID. */
	private static final long serialVersionUID = 6411527075103472113L;

	public Pair(final K key, final V value) {
		super(key, value);
	}
}