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:
import java.lang.*;
import java.math.*;
import java.util.*;
import java.io.*;

public class Main {
    class Node implements Comparable<Node>{
        int x;
        int d;
        public Node(int x,int d){
            this.x=x;
            this.d=d;
        }
        public int compareTo(Node c){
            int t=Integer.compare(this.d,c.d);
            return t;
        }
    }
    void solve(){
        n=ni(); k=ni();
        g=new int[n+1][];
        int from[]=new int[n+1];
        int to[]=new int[n+1];
        int cnt[]=new int[n+1];
        for(int i=1;i<n;i++){
            int x=ni(),y=ni();
            from[i]=x; to[i]=y;
            cnt[x]++;
            cnt[y]++;
        }
        for(int i=1;i<=n;i++) g[i]=new int[cnt[i]];
        for(int i=1;i<n;i++){
            g[from[i]][--cnt[from[i]]]=to[i];
            g[to[i]][--cnt[to[i]]]=from[i];
        }

        int root=-1;
        for(int i=1;i<=n;i++) {
            if(g[i].length>1){
                root=i;
                break;
            }
        }
        mx=new int[n+1];

        dfs(root,-1);
        dfs2(root,-1);
        if(mx[root]>0 || g[root].length==1) ans++;
        pw.println(ans);
    }
    int n,k;
    int g[][];
    int mx[];
    static ArrayList<Integer> vec=new ArrayList<>(1000000);
    void dfs(int v,int pr){

        for(int u : g[v]){
            if(u!=pr) {
                dfs(u,v);
                mx[v]=Math.max(mx[v],mx[u]+1);
            }
        }

    }
    int ans=0;
    int id;
    void dfs2(int v,int pr){

        for(int u : g[v]){
            if(u!=pr){
                dfs2(u,v);
            }
        }

        vec.clear();
        for(int u : g[v]){
            if(u!=pr && mx[u]!=-1) vec.add(mx[u]+1);
        }
        if(g[v].length==1) return;
        vec.add(0);
        Collections.sort(vec);

        for( id=vec.size()-1;id>0;id--){
            if(vec.get(id)+vec.get(id-1)>k) ans++;
            else break;
        }
        if(id==0) mx[v]=-1;
        else
        mx[v]=vec.get(id);
        vec.clear();


    }
    long M=(long)1e9+7;
    InputStream is;
    PrintWriter pw;
    String INPUT = "";
    void run() throws Exception {
        is = is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        pw = new PrintWriter(System.out);

        Thread t = new Thread(null, null, "~", Runtime.getRuntime().maxMemory()){
            @Override
            public void run() {
                long s = System.currentTimeMillis();
                solve();

                pw.flush();
                if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
            }
        };
        t.start();
        t.join();
    }

    public static void main(String[] args) throws Exception { new Main().run(); }

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

    private 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 boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
    private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }

    private double nd() { return Double.parseDouble(ns()); }
    private char nc() { return (char)skip(); }

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

    private 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 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 boolean oj = System.getProperty("ONLINE_JUDGE") != null;
    private void tr(Object... o) { if(INPUT.length() > 0)System.out.println(Arrays.deepToString(o)); }

}