Problem: You are given an undirected tree, consisting of n vertices.

The vertex is called a leaf if it has exactly one vertex adjacent to it.

The distance between some pair of vertices is the number of edges in the shortest path between them.

Let's call some set of leaves beautiful if the maximum distance between any pair of leaves in it is less or equal to k.

You want to split all leaves into non-intersecting beautiful sets. What is the minimal number of sets in such a split?

Input

The first line contains two integers n and k (3 ≤ n ≤ 10^6, 1 ≤ k ≤ 10^6) — the number of vertices in the tree and the maximum distance between any pair of leaves in each beautiful set.

Each of the next n - 1 lines contains two integers v_i and u_i (1 ≤ v_i, u_i ≤ n) — the description of the i-th edge. 

It is guaranteed that the given edges form a tree.

Output

Print a single integer — the minimal number of beautiful sets the split can have. 

Examples

Input

9 3
1 2
1 3
2 4
2 5
3 6
6 7
6 8
3 9


Output

2


Input

5 3
1 2
2 3
3 4
4 5


Output

2


Input

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


Output

5

Note

Here is the graph for the first example:

<image>

Solution (in JAVA):

Solution:
//stan hu tao
//join nct ridin by first year culture reps
import static java.lang.Math.max;
import static java.lang.Math.min;
import static java.lang.Math.abs;
import java.util.*;
import java.io.*;
import java.math.*;

public class x1042F
{
    static int[][] edges;
    public static void main(String hi[]) throws Exception
    {
        BufferedReader infile = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(infile.readLine());
        int N = Integer.parseInt(st.nextToken());
        int K = Integer.parseInt(st.nextToken());
        int[] freq = new int[N];
        int[] freqq = new int[N];
        ArrayDeque<Integer> input = new ArrayDeque<Integer>();
        for(int i=1; i < N; i++)
        {
            st = new StringTokenizer(infile.readLine());
            int a = Integer.parseInt(st.nextToken())-1;
            int b = Integer.parseInt(st.nextToken())-1;
            freq[a]++;  freq[b]++;
            freqq[a]++; freqq[b]++;
            input.add(a);   input.add(b);
        }
        edges = new int[N][];
        for(int i=0; i < N; i++)
            edges[i] = new int[freqq[i]];
        while(input.size() > 0)
        {
            int a = input.poll();
            int b = input.poll();
            edges[a][--freqq[a]] = b;
            edges[b][--freqq[b]] = a;
        }
        int root = 0;
        for(int v=0; v < N; v++)
            if(edges[v].length >= 2)
                root = v;
        //gen depths
        int[] depth = new int[N];
        ArrayDeque<Integer> q = new ArrayDeque<Integer>();
        q.add(root);    q.add(-1);
        while(q.size() > 0)
        {
            int curr = q.poll();
            int par = q.poll();
            for(int next: edges[curr])
                if(next != par)
                {
                    q.add(next);    q.add(curr);
                    depth[next] = depth[curr]+1;
                }
        }
        int[] vals = new int[N];
        ArrayList<Integer> lis = new ArrayList<Integer>();
        for(int i=0; i < N; i++)
            lis.add(i);
        Collections.sort(lis, (x,y) -> {
            return depth[y]-depth[x];
        });
        int res = 1;
        for(int curr: lis)
        {
            if(edges[curr].length > 1)
            {
                ArrayList<Integer> ls = new ArrayList<Integer>();
                for(int next: edges[curr])
                    if(depth[next] == depth[curr]+1)
                        ls.add(vals[next]+1);
                Collections.sort(ls);
                vals[curr] = -69;
                for(int i=ls.size()-1; i > 0; i--)
                {
                    if(ls.get(i)+ls.get(i-1) <= K)
                    {
                        vals[curr] = ls.get(i);
                        break;
                    }
                    res++;
                }
                if(vals[curr] == -69)
                    vals[curr] = ls.get(0);
            }
        }
        System.out.println(res);
    }
}
class FastScanner
{
    private int BS = 1 << 16;
    private char NC = (char) 0;
    private byte[] buf = new byte[BS];
    private int bId = 0, size = 0;
    private char c = NC;
    private double cnt = 1;
    private BufferedInputStream in;

    public FastScanner() {
        in = new BufferedInputStream(System.in, BS);
    }

    public FastScanner(String s) {
        try {
            in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
        } catch (Exception e) {
            in = new BufferedInputStream(System.in, BS);
        }
    }

    private char getChar() {
        while (bId == size) {
            try {
                size = in.read(buf);
            } catch (Exception e) {
                return NC;
            }
            if (size == -1) return NC;
            bId = 0;
        }
        return (char) buf[bId++];
    }

    public int nextInt() {
        return (int) nextLong();
    }

    public int[] nextInts(int N) {
        int[] res = new int[N];
        for (int i = 0; i < N; i++) {
            res[i] = (int) nextLong();
        }
        return res;
    }

    public long[] nextLongs(int N) {
        long[] res = new long[N];
        for (int i = 0; i < N; i++) {
            res[i] = nextLong();
        }
        return res;
    }

    public long nextLong() {
        cnt = 1;
        boolean neg = false;
        if (c == NC) c = getChar();
        for (; (c < '0' || c > '9'); c = getChar()) {
            if (c == '-') neg = true;
        }
        long res = 0;
        for (; c >= '0' && c <= '9'; c = getChar()) {
            res = (res << 3) + (res << 1) + c - '0';
            cnt *= 10;
        }
        return neg ? -res : res;
    }

    public double nextDouble() {
        double cur = nextLong();
        return c != '.' ? cur : cur + nextLong() / cnt;
    }

    public double[] nextDoubles(int N) {
        double[] res = new double[N];
        for (int i = 0; i < N; i++) {
            res[i] = nextDouble();
        }
        return res;
    }

    public String next() {
        StringBuilder res = new StringBuilder();
        while (c <= 32) c = getChar();
        while (c > 32) {
            res.append(c);
            c = getChar();
        }
        return res.toString();
    }

    public String nextLine() {
        StringBuilder res = new StringBuilder();
        while (c <= 32) c = getChar();
        while (c != '\n') {
            res.append(c);
            c = getChar();
        }
        return res.toString();
    }

    public boolean hasNext() {
        if (c > 32) return true;
        while (true) {
            c = getChar();
            if (c == NC) return false;
            else if (c > 32) return true;
        }
    }
}