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 Java7 (OpenJDK 1.7.0) (judge verdict: Wrong Answer)


import java.util.Arrays;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {

		//		ABC115_A();
		//		ABC115_B();
		ABC115_C();
		// ABC115_D();
	}

	private static void ABC115_A() {
		Scanner scanner = null;
		int date = 0;

		try {
			scanner = new Scanner(System.in);
			date = scanner.nextInt();

			switch (date) {
			case 22:
				System.out.println("Christmas Eve Eve Eve");
				break;
			case 23:
				System.out.println("Christmas Eve Eve");
				break;
			case 24:
				System.out.println("Christmas Eve");
				break;
			case 25:
				System.out.println("Christmas");
				break;
			default:
				System.out.println("fail!");
				break;
			}

		} finally {
			if (scanner != null) {
				scanner.close();
			}
		}
	}

	private static void ABC115_B() {
		Scanner scanner = null;
		int numItem = 0;
		int priceItem = 0;

		try {
			scanner = new Scanner(System.in);
			numItem = scanner.nextInt();
			int[] priceArray = new int[numItem];

			for (int i = 0; i < numItem; i++) {
				priceArray[i] = scanner.nextInt();
			}

			Arrays.sort(priceArray);

			int prices = 0;
			for (int i = 0; i < priceArray.length; i++) {
				if (i != numItem - 1) {
					prices += priceArray[i];
				} else {
					prices += priceArray[i] / 2;
				}

			}

			System.out.println(prices);

		} finally {
			if (scanner != null) {
				scanner.close();
			}
		}
	}

	private static void ABC115_C() {
		Scanner scanner = null;
		int totalTreeNum = 0;
		int selectedTreeNum = 0;

		try {
			scanner = new Scanner(System.in);
			totalTreeNum = scanner.nextInt();
			selectedTreeNum = scanner.nextInt();

			int[] treeTehightList = new int[totalTreeNum];

			for (int i = 0; i < totalTreeNum; i++) {
				treeTehightList[i] = scanner.nextInt();
			}

			Arrays.sort(treeTehightList);

			//			int[] sabunList = new int[treeTehightList.length - 1];

			//			for (int i = 0; i < sabunList.length; i++) {
			//				sabunList[i] = treeTehightList[i + 1] - treeTehightList[i];
			//			}
			int minDiff = 0;
			for (int i = 0; i < treeTehightList.length - (selectedTreeNum - 1); i++) {
				if (i == 0) {
					minDiff = treeTehightList[i];
				}
				if (minDiff > treeTehightList[i + selectedTreeNum - 1] - treeTehightList[i]) {
					minDiff = treeTehightList[i + selectedTreeNum - 1] - treeTehightList[i];
				}

			}
			System.out.println(minDiff);

		} finally {
			if (scanner != null) {
				scanner.close();
			}
		}
	}

	public static class Res {
		private int start;

		public void setStart(int start) {
			this.start = start;
		}

		public void setEnd(int end) {
			this.end = end;
		}

		private int end;
		int[] heightList;

		public Res(int s, int e, int[] heightList) {
			this.start = s;
			this.end = e;
			this.heightList = heightList;
		}

		public int getStart() {
			return start;
		}

		public int getEnd() {
			return end;
		}

		public int getSabun() {
			return heightList[end] - heightList[start];
		}
	}

	private static Res getMaxSabunNo(int[] sabunList, Res resint, int selectedTreeNum) {
		int maxSabun = 0;
		int maxSabunNo = resint.getStart();
		for (int i = resint.getStart(); i < resint.getEnd(); i++) {
			if (maxSabun < sabunList[i]) {
				maxSabun = sabunList[i];
				maxSabunNo = i;

			}
		}
		if (maxSabunNo + 1 >= selectedTreeNum) {
			resint.setEnd(maxSabunNo);
			resint = getMaxSabunNo(sabunList, resint, selectedTreeNum);
		} else if (sabunList.length - maxSabunNo >= selectedTreeNum) {
			resint.setStart(maxSabunNo);
			resint = getMaxSabunNo(sabunList, resint, selectedTreeNum);
		} else {
			resint.setEnd(maxSabunNo);
		}

		return resint;
	}

	private static void ABC115_D() {
		Scanner scanner = null;
		int lineAB = 0;
		int lineBC = 0;
		int lineCA = 0;

		try {
			scanner = new Scanner(System.in);
			lineAB = scanner.nextInt();

			System.out.println("");

		} finally {
			if (scanner != null) {
				scanner.close();
			}
		}
	}
}