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.Arrays;
import java.util.NoSuchElementException;

public class Main {

	static int n;
	static int k;
	static long[] h;
	public static void main(String[] args) {
		FastScanner scan = new FastScanner();
		PrintWriter out = new PrintWriter(System.out);
		n = scan.nextInt();
		k = scan.nextInt();
		h = new long[n];
		int i;
		for(i = 0; i < n; i++)
			h[i] = scan.nextLong();

		Arrays.sort(h);

		long min = Long.MAX_VALUE;
		for(i = k - 1; i < n; i++)
			min = Math.min(min, h[i] - h[i - k + 1]);
		out.print(min);
		out.close();
	}
}

class cal {
	long mod;

	cal(long x) {
		this.mod = x;
	}

	long mpow(long x, long n) {
		if (n == 0)
			return 1;
		if (n % 2 == 0) {
			long root = mpow(x, n / 2);
			return root * root % mod;
		} else {
			return x * mpow(x, n - 1) % mod;
		}
	}

	long mcomb(long a, long b) {
		if (b > a - b)
			return mcomb(a, a - b);
		long m = 1;
		long d = 1;
		long i;
		for (i = 0; i < b; i++) {
			m *= (a - i);
			m %= mod;
			d *= (i + 1);
			d %= mod;
		}
		long ans = m * mpow(d, mod - 2) % mod;

		return ans;
	}
}

class unionFind {
	int[] par;
	int[] size;

	unionFind(int x) {
		this.par = new int[x + 1];
		this.size = new int[x + 1];

		int i;
		for (i = 0; i <= x; i++)
			this.par[i] = i;
		Arrays.fill(this.size, 1);
	}

	int root(int x) {
		int r = x;
		while (r != this.par[r]) {
			r = this.par[r];
		}

		return r;
	}

	void union(int x, int y) {
		int rx = root(x);
		int ry = root(y);
		if (rx == ry)
			return;

		if (this.size[rx] < this.size[ry]) {
			this.size[ry] += this.size[rx];
			this.par[rx] = ry;
		} else {
			this.size[rx] += this.size[ry];
			this.par[ry] = rx;
		}
	}

	int size(int x) {
		return this.size[root(x)];
	}

	boolean same(int x, int y) {
		int rx = root(x);
		int ry = root(y);

		return rx == ry;
	}
}

class FastScanner {
	private final InputStream in = System.in;
	private final byte[] buffer = new byte[1024];
	private int ptr = 0;
	private int buflen = 0;

	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;
	}

	private int readByte() {
		if (hasNextByte())
			return buffer[ptr++];
		else
			return -1;
	}

	private static boolean isPrintableChar(int c) {
		return 33 <= c && c <= 126;
	}

	public boolean hasNext() {
		while (hasNextByte() && !isPrintableChar(buffer[ptr]))
			ptr++;
		return hasNextByte();
	}

	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();
	}

	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();
		}
	}

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

	public double nextDouble() {
		return Double.parseDouble(next());
	}
}