Problem:
Score : 600 points

Problem Statement

Given an undirected tree, let the distance between vertices u and v be the
number of edges on the simple path from u to v.
The diameter of a tree is the maximum among the distances between any two vertices.
We will call a tree good if and only if its diameter is at most K.

You are given an undirected tree with N vertices numbered 1 through N.
For each i (1≦i≦N-1), there is an edge connecting vertices A_i and B_i.

You want to remove zero or more vertices from the tree, so that the resulting tree is good.
When a vertex is removed, all incident edges will also be removed.
The resulting graph must be connected.

Find the minimum number of vertices that you need to remove in order to produce a good tree.

Constraints

2≦N≦2000

1≦K≦N-1

1≦A_i≦N, 1≦B_i≦N

The graph defined by A_i and B_i is a tree.

Input

The input is given from Standard Input in the following format:

N K
A_1 B_1
A_2 B_2
:
A_{N-1} B_{N-1}

Output

Print the minimum number of vertices that you need to remove in order to produce a good tree.

Sample Input 1

6 2
1 2
3 2
4 2
1 6
5 6

Sample Output 1

2

The tree is shown below. Removing vertices 5 and 6 will result in a good tree with the diameter of 2.

Sample Input 2

6 5
1 2
3 2
4 2
1 6
5 6

Sample Output 2

0

Since the given tree is already good, you do not need to remove any vertex.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.InputMismatchException;

public class Main {
	static InputStream is;
	static PrintWriter out;
	static String INPUT = "";

	void solve() {
		int n = ni(), k = ni();
		ArrayList<Integer> to[] = new ArrayList[n];
		for (int i = 0; i < n; ++i)
			to[i] = new ArrayList<>();
		for (int i = 0; i + 1 < n; ++i) {
			int a = ni() - 1, b = ni() - 1;
			to[a].add(b);
			to[b].add(a);
		}
		int dist[][] = new int[n][];
		for (int i = 0; i < n; ++i) {
			dist[i] = max(n, i, to);
		}
		int res = Integer.MAX_VALUE;
		for (int i = 0; i < n; ++i) {
			if ((k & 1) == 0) {
				int t = 0;
				for (int j = 0; j < n; ++j) {
					if (dist[i][j] > k / 2) ++t;
				}
				if (res > t) res = t;
			} else {
				for (Integer j : to[i]) {
					int t = 0;
					for (int z = 0; z < n; ++z) {
						if (Math.min(dist[i][z], dist[j][z]) > k / 2) ++t;
					}
					if (res > t) res = t;
				}
			}
		}
		out.println(res);
	}

	int[] max(int n, int x, ArrayList<Integer> to[]) {
		int d[] = new int[n];
		Arrays.fill(d, -1);
		d[x] = 0;
		int l = -1, m = 0, q[] = new int[n], qi = 0, qs = 1;
		q[0] = x;
		while (qi < qs) {
			int s = q[qi++];
			for (Integer g : to[s]) {
				if (d[g] == -1) {
					d[g] = d[s] + 1;
					q[qs++] = g;
					if (m < d[g]) {
						m = d[g];
						l = g;
					}
				}
			}
		}
		return d;
	}

	long gcd(long a, long b) {
		return b == 0 ? a : gcd(b, a % b);
	}

	public static void main(String[] args) throws Exception {
		long S = System.currentTimeMillis();
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);

		new Main().solve();
		out.flush();
		long G = System.currentTimeMillis();
		tr(G - S + "ms");
	}

	private static boolean eof() {
		if (lenbuf == -1) return true;
		int lptr = ptrbuf;
		while (lptr < lenbuf)
			if (!isSpaceChar(inbuf[lptr++])) return false;

		try {
			is.mark(1000);
			while (true) {
				int b = is.read();
				if (b == -1) {
					is.reset();
					return true;
				} else if (!isSpaceChar(b)) {
					is.reset();
					return false;
				}
			}
		} catch (IOException e) {
			return true;
		}
	}

	private static byte[] inbuf = new byte[1024];
	static int lenbuf = 0, ptrbuf = 0;

	private static int readByte() {
		if (lenbuf == -1) throw new InputMismatchException();
		if (ptrbuf >= lenbuf) {
			ptrbuf = 0;
			try {
				lenbuf = is.read(inbuf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (lenbuf <= 0) return -1;
		}
		return inbuf[ptrbuf++];
	}

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

	private static int skip() {
		int b;
		while ((b = readByte()) != -1 && isSpaceChar(b))
			;
		return b;
	}

	private static double nd() {
		return Double.parseDouble(ns());
	}

	private static char nc() {
		return (char) skip();
	}

	private static String ns() {
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	private static char[] ns(int n) {
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while (p < n && !(isSpaceChar(b))) {
			buf[p++] = (char) b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}

	private static char[][] nm(int n, int m) {
		char[][] map = new char[n][];
		for (int i = 0; i < n; i++)
			map[i] = ns(m);
		return map;
	}

	private static int[] na(int n) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = ni();
		return a;
	}

	private static int ni() {
		int num = 0, b;
		boolean minus = false;
		while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
			;
		if (b == '-') {
			minus = true;
			b = readByte();
		}

		while (true) {
			if (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
			} else {
				return minus ? -num : num;
			}
			b = readByte();
		}
	}

	private static long nl() {
		long num = 0;
		int b;
		boolean minus = false;
		while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
			;
		if (b == '-') {
			minus = true;
			b = readByte();
		}

		while (true) {
			if (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
			} else {
				return minus ? -num : num;
			}
			b = readByte();
		}
	}

	private static void tr(Object... o) {
		if (INPUT.length() != 0) System.out.println(Arrays.deepToString(o));
	}

	private static void debug(Object... o) {
		System.out.println(Arrays.deepToString(o));
	}
}