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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;

class Program
{
    const int M = 1000000007;
    const double eps = 1e-9;
    static int[] dd = { 0, 1, 0, -1, 0 };
    static void Main()
    {
        var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        var sc = new Scan();
        int n, k;
        sc.Multi(out n, out k);
        var edge = new List<int>[n];
        var a = new int[n - 1][];
        for (int i = 0; i < n; i++)
            edge[i] = new List<int>();

        for (int i = 0; i < n - 1; i++)
        {
            a[i] = sc.IntArr.Select(x => x - 1).ToArray();
            edge[a[i][0]].Add(a[i][1]);
            edge[a[i][1]].Add(a[i][0]);
        }
        int lim = k >> 1;
        int min = n;
        var q = new Queue<int>();
        if (k % 2 == 0)
        {
            for (int i = 0; i < n; i++)
            {
                var dist = new int[n];
                for (int j = 0; j < n; j++)
                    dist[j] = -1;

                int c = 1;
                dist[i] = 0;
                q.Enqueue(i);
                while (q.Any())
                {
                    int p = q.Dequeue();
                    if (dist[p] >= lim)
                    {
                        q.Clear();
                        break;
                    }
                    foreach (var item in edge[p])
                    {
                        if (dist[item] < 0)
                        {
                            dist[item] = dist[p] + 1;
                            ++c;
                            q.Enqueue(item);
                        }
                    }
                }
                min = Math.Min(min, n - c);
            }
        }
        else
        {
            foreach (var i in a)
            {
                var dist = new int[n];
                for (int j = 0; j < n; j++)
                    dist[j] = -1;

                int c = 2;
                dist[i[0]] = 0;
                dist[i[1]] = 0;
                q.Enqueue(i[0]);
                while (q.Any())
                {
                    int p = q.Dequeue();
                    if (dist[p] >= lim)
                    {
                        q.Clear();
                        break;
                    }

                    foreach (var item in edge[p])
                    {
                        if (dist[item] < 0)
                        {
                            dist[item] = dist[p] + 1;
                            ++c;
                            q.Enqueue(item);
                        }
                    }
                }
                q.Enqueue(i[1]);
                while (q.Any())
                {
                    int p = q.Dequeue();
                    if (dist[p] >= lim)
                    {
                        q.Clear();
                        break;
                    }

                    foreach (var item in edge[p])
                    {
                        if (dist[item] < 0)
                        {
                            dist[item] = dist[p] + 1;
                            ++c;
                            q.Enqueue(item);
                        }
                    }
                }
                min = Math.Min(min, n - c);
            }
        }
        sw.WriteLine(min);
        sw.Flush();
    }

    static void swap<T>(ref T a, ref T b) { var t = a; a = b; b = t; }
    static void swap<T>(IList<T> a, int i, int j) { var t = a[i]; a[i] = a[j]; a[j] = t; }
    static T Max<T>(params T[] a) { return a.Max(); }
    static T Min<T>(params T[] a) { return a.Min(); }
    static void DBG<T>(params T[] a) { Console.WriteLine(string.Join(" ", a)); }
    static void DBG(params object[] a) { Console.WriteLine(string.Join(" ", a)); }
    static T[] copy<T>(IList<T> a)
    {
        var ret = new T[a.Count];
        for (int i = 0; i < a.Count; i++) ret[i] = a[i];
        return ret;
    }
}
class Scan
{
    public int Int { get { return int.Parse(Str); } }
    public long Long { get { return long.Parse(Str); } }
    public double Double { get { return double.Parse(Str); } }
    public string Str { get { return Console.ReadLine().Trim(); } }
    public int[] IntArr { get { return StrArr.Select(int.Parse).ToArray(); } }
    public int[] IntArrWithSep(char sep) { return Str.Split(sep).Select(int.Parse).ToArray(); }
    public long[] LongArr { get { return StrArr.Select(long.Parse).ToArray(); } }
    public double[] DoubleArr { get { return StrArr.Select(double.Parse).ToArray(); } }
    public string[] StrArr { get { return Str.Split(); } }
    T cv<T>(string inp)
    {
        if (typeof(T).Equals(typeof(int)))    return (T)Convert.ChangeType(int.Parse(inp), typeof(T));
        if (typeof(T).Equals(typeof(long)))   return (T)Convert.ChangeType(long.Parse(inp), typeof(T));
        if (typeof(T).Equals(typeof(double))) return (T)Convert.ChangeType(double.Parse(inp), typeof(T));
        if (typeof(T).Equals(typeof(char)))   return (T)Convert.ChangeType(inp[0], typeof(T));
        return (T)Convert.ChangeType(inp, typeof(T));
    }
    public void Multi<T>(out T a) { a = cv<T>(Str); }
    public void Multi<T, U>(out T a, out U b)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); }
    public void Multi<T, U, V>(out T a, out U b, out V c)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); }
    public void Multi<T, U, V, W>(out T a, out U b, out V c, out W d)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); }
    public void Multi<T, U, V, W, X>(out T a, out U b, out V c, out W d, out X e)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]); }
}
class mymath
{
    static int Mod = 1000000007;
    public void setMod(int m) { Mod = m; }
    public bool isprime(long a)
    {
        if (a < 2) return false;
        for (long i = 2; i * i <= a; i++) if (a % i == 0) return false;
        return true;
    }
    public bool[] sieve(int n)
    {
        var isp = new bool[n + 1];
        for (int i = 2; i <= n; i++) isp[i] = true;
        for (int i = 2; i * i <= n; i++) if (isp[i]) for (int j = i * i; j <= n; j += i) isp[j] = false;
        return isp;
    }
    public List<int> getprimes(int n)
    {
        var prs = new List<int>();
        var isp = sieve(n);
        for (int i = 2; i <= n; i++) if (isp[i]) prs.Add(i);
        return prs;
    }
    public long[][] E(int n)
    {
        var ret = new long[n][];
        for (int i = 0; i < n; i++)
        {
            ret[i] = new long[n];
            ret[i][i] = 1;
        }
        return ret;
    }
    public long[][] powmat(long[][] A, long n)
    {
        if (n == 0) return E(A.Length);
        var t = powmat(A, n / 2);
        if ((n & 1) == 0) return mulmat(t, t);
        return mulmat(mulmat(t, t), A);
    }
    public long[] mulmat(long[][] A, long[] x)
    {
        int n = A.Length, m = x.Length;
        var ans = new long[n];
        for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) ans[i] = (ans[i] + x[j] * A[i][j]) % Mod;
        return ans;
    }
    public long[][] mulmat(long[][] A, long[][] B)
    {
        int n = A.Length, m = B[0].Length, l = B.Length;
        var ans = new long[n][];
        for (int i = 0; i < n; i++)
        {
            ans[i] = new long[m];
            for (int j = 0; j < m; j++) for (int k = 0; k < l; k++) ans[i][j] = (ans[i][j] + A[i][k] * B[k][j]) % Mod;
        }
        return ans;
    }
    public long[] addmat(long[] x, long[] y)
    {
        int n = x.Length;
        var ans = new long[n];
        for (int i = 0; i < n; i++) ans[i] = (x[i] + y[i]) % Mod;
        return ans;
    }
    public long[][] addmat(long[][] A, long[][] B)
    {
        int n = A.Length, m = A[0].Length;
        var ans = new long[n][];
        for (int i = 0; i < n; i++) ans[i] = addmat(A[i], B[i]);
        return ans;
    }
    public long powmod(long a, long b)
    {
        if (a >= Mod) return powmod(a % Mod, b);
        if (a == 0) return 0;
        if (b == 0) return 1;
        var t = powmod(a, b / 2);
        if ((b & 1) == 0) return t * t % Mod;
        return t * t % Mod * a % Mod;
    }
    public long inv(long a) { return powmod(a, Mod - 2); }
    public long gcd(long a, long b)
    {
        while (b > 0) { var t = a % b; a = b; b = t; }
        return a;
    }
    public long lcm(long a, long b) { return a * (b / gcd(a, b)); }
    public long Comb(int n, int r)
    {
        if (n < 0 || r < 0 || r > n) return 0;
        if (n - r < r) r = n - r;
        if (r == 0) return 1;
        if (r == 1) return n;
        var numerator = new int[r];
        var denominator = new int[r];
        for (int k = 0; k < r; k++)
        {
            numerator[k] = n - r + k + 1;
            denominator[k] = k + 1;
        }
        for (int p = 2; p <= r; p++)
        {
            int pivot = denominator[p - 1];
            if (pivot > 1)
            {
                int offset = (n - r) % p;
                for (int k = p - 1; k < r; k += p)
                {
                    numerator[k - offset] /= pivot;
                    denominator[k] /= pivot;
                }
            }
        }
        long result = 1;
        for (int k = 0; k < r; k++) if (numerator[k] > 1) result = result * numerator[k] % Mod;
        return result;
    }
}