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: Wrong Answer)

import java.io.*;
import java.math.*;
import java.util.*;
import java.util.Map.Entry;


class Main {
	static Node[] node;
	public static void main(String[] args) {	
		//FastScanner sc = new FastScanner();
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int K = sc.nextInt();
		int[] A = new int[N-1];
		int[] B = new int[N-1];
		for(int i = 0; i < N-1; i++) {
			A[i] = sc.nextInt();
			B[i] = sc.nextInt();
		}
		node = new Node[N];
		for(int i = 0; i < N; i++) {
			node[i] = new Node();
		}
		for(int i = 0; i < N-1; i++) {
			node[A[i] - 1].dst.add(B[i] - 1);
			node[B[i] - 1].dst.add(A[i] - 1);
		}
		int count = 0;
		while(true) {
			Data tmp = diameter();
			if(tmp.length <= K) break;
			node[tmp.maxID].rem = true;
			count++;
		}
		System.out.println(count);
	}

    
	static Data diameter() {
		int[] min = new int[node.length];
		boolean[] cantRemove = new boolean[node.length];
		for(int i = 0; i < node.length; i++) {
			if(node[i].rem) cantRemove[i] = true;
			ArrayList<Integer> next = node[i].dst;
			int count = 0;
			for(int j = 0; j < next.size(); j++) {
				if(!node[next.get(j)].rem) count++;
			}
			if(count >= 2) cantRemove[i] = true;
		}
		Arrays.fill(min, 2 << 28);
		ArrayDeque<P> q = new ArrayDeque<>();
		for(int i = 0; i < node.length; i++) {
			if(!node[i].rem) {
				q.addFirst(new P(i,0));
				break;
			}
		}
		int maxP = 0;
		int maxL = 0;
		while(!q.isEmpty()) {
			P p = q.pollLast();
			if(min[p.now] <= p.cost) continue;
			min[p.now] = p.cost;
			if(maxL < p.cost) {
				maxL = p.cost;
				maxP = p.now;
			}
			for(int i = 0; i < node[p.now].dst.size(); i++) {
				if(!node[node[p.now].dst.get(i)].rem) q.addFirst(new P(node[p.now].dst.get(i),p.cost+1));
			}
		}
		Arrays.fill(min, 2 << 28);
		q.addFirst(new P(maxP,0));
		maxP = 0;
		maxL = 0;
		int maxLL = 0;
		while(!q.isEmpty()) {
			P p = q.pollLast();
			if(min[p.now] <= p.cost) continue;
			min[p.now] = p.cost;
			if(maxLL < p.cost) {
				maxLL = p.cost;
				
			}
			if(maxL < p.cost && !cantRemove[p.now]) {
				maxL = p.cost;
				maxP = p.now;
			}
			for(int i = 0; i < node[p.now].dst.size(); i++) {
				if(!node[node[p.now].dst.get(i)].rem) q.addFirst(new P(node[p.now].dst.get(i),p.cost+1));
			}
		}
		return new Data(maxP,maxLL);
	}
	static class P {
		int now;
		int cost;
		P(int a, int b) {
			now = a;
			cost = b;
		}
	}
	static class Data {
		int maxID;
		int length; 
		Data(int a, int b) {
			maxID = a;
			length = b;
		}
	}
	static class Node {
		boolean rem = false;
		ArrayList<Integer> dst = new ArrayList<>();
	}
	


	
	static 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;}
	    private void skipUnprintable() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;}
	    public boolean hasNext() { skipUnprintable(); 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() {
	        if (!hasNext()) throw new NoSuchElementException();
	        int 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();
	        }
	    }
	}
}