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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.ArrayList;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;
/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Alex
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        C solver = new C();
        solver.solve(1, in, out);
        out.close();
    }
    static class C {
        int n;
        int k;
        ArrayList<Integer>[] adj;
        int vertexdfs(int cur, int prev, int moar) {
            if (moar < 0) return 0;
            int res = 1;
            for (int nxt : adj[cur])
                if (nxt != prev) {
                    res += vertexdfs(nxt, cur, moar - 1);
                }
            return res;
        }
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            n = in.readInt(); // [2, 2000]
            k = in.readInt();
            int res = Integer.MAX_VALUE;
            ArrayList<Integer>[] adj = new ArrayList[n];
            IntIntPair[] edges = new IntIntPair[n - 1];
            for (int i = 0; i < adj.length; i++)
                adj[i] = new ArrayList<>();
            for (int i = 0; i < n - 1; i++) {
                int a = in.readInt() - 1;
                int b = in.readInt() - 1;
                adj[a].add(b);
                adj[b].add(a);
                edges[i] = new IntIntPair(a, b);
            }
            this.adj = adj;
            for (int start = 0; start < n; start++) {
                res = Math.min(res, n - vertexdfs(start, -1, k / 2));
            }
            for (int start = 0; start < n - 1; start++) {
                int tmp = n - vertexdfs(edges[start].first, edges[start].second, (k - 1) / 2) -
                        vertexdfs(edges[start].second, edges[start].first, (k - 1) / 2);
                res = Math.min(res, tmp);
            }
            out.printLine(res);
        }
    }
    static class IntIntPair implements Comparable<IntIntPair> {
        public final int first;
        public final int second;
        public IntIntPair(int first, int second) {
            this.first = first;
            this.second = second;
        }
        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            IntIntPair pair = (IntIntPair) o;
            return first == pair.first && second == pair.second;
        }
        public int hashCode() {
            int result = Integer.hashCode(first);
            result = 31 * result + Integer.hashCode(second);
            return result;
        }
        public String toString() {
            return "(" + first + "," + second + ")";
        }
        @SuppressWarnings ({"unchecked"})
        public int compareTo(IntIntPair o) {
            int value = Integer.compare(first, o.first);
            if (value != 0) {
                return value;
            }
            return Integer.compare(second, o.second);
        }
    }
    static class OutputWriter {
        private final PrintWriter writer;
        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }
        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }
        public void close() {
            writer.close();
        }
        public void printLine(int i) {
            writer.println(i);
        }
    }
    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;
        public InputReader(InputStream stream) {
            this.stream = stream;
        }
        public int read() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }
        public int readInt() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return isWhitespace(c);
        }
        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }
}