Someone give a strange birthday present to Ivan. It is hedgehog — connected undirected graph in which one vertex has degree at least 3 (we will call it center) and all other vertices has degree 1. Ivan thought that hedgehog is too boring and decided to make himself k-multihedgehog.

Let us define k-multihedgehog as follows:

  * 1-multihedgehog is hedgehog: it has one vertex of degree at least 3 and some vertices of degree 1.
  * For all k ≥ 2, k-multihedgehog is (k-1)-multihedgehog in which the following changes has been made for each vertex v with degree 1: let u be its only neighbor; remove vertex v, create a new hedgehog with center at vertex w and connect vertices u and w with an edge. New hedgehogs can differ from each other and the initial gift. 



Thereby k-multihedgehog is a tree. Ivan made k-multihedgehog but he is not sure that he did not make any mistakes. That is why he asked you to check if his tree is indeed k-multihedgehog.

Input

First line of input contains 2 integers n, k (1 ≤ n ≤ 10^{5}, 1 ≤ k ≤ 10^{9}) — number of vertices and hedgehog parameter.

Next n-1 lines contains two integers u v (1 ≤ u,    v ≤ n;    u ≠ v) — indices of vertices connected by edge.

It is guaranteed that given graph is a tree.

Output

Print "Yes" (without quotes), if given graph is k-multihedgehog, and "No" (without quotes) otherwise.

Examples

Input

14 2
1 4
2 4
3 4
4 13
10 5
11 5
12 5
14 5
5 13
6 7
8 6
13 6
9 6


Output

Yes


Input

3 1
1 3
2 3


Output

No

Note

2-multihedgehog from the first example looks like this:

<image>

Its center is vertex 13. Hedgehogs created on last step are: [4 (center), 1, 2, 3], [6 (center), 7, 8, 9], [5 (center), 10, 11, 12, 13].

Tree from second example is not a hedgehog because degree of center should be at least 3.
//package contests.CF1067;

import java.io.*;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class B {

    static ArrayList<Integer>[] adjj;
    static ArrayList<Edge>[] adj;

    static int check(int u, int p, int lvl){
        if(p == -1) {
            if (adjj[u].size() < 3)
                return -1;
        }else
            if(adjj[u].size() < 4)
                return -1;

        int maxLvl = -2;
        for (int v: adjj[u]) {
            if(v == p)
                continue;
            int a = check(v, u, lvl+1);
            if(maxLvl == -2)
                maxLvl = a;
            else
                if(maxLvl != a)
                    return -1;
        }
        if(maxLvl == -1)
            return 0;
        return maxLvl;
    }
    public static void main(String[] args) throws IOException{
        Scanner sc = new Scanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);

        int n = sc.nextInt();
        adj = new ArrayList[n];
        adjj = new ArrayList[n];
        int k = sc.nextInt();
        for (int i = 0; i < adj.length; i++) {
            adj[i] = new ArrayList<>();
            adjj[i] = new ArrayList<>();
        }

        boolean vis[] = new boolean[n];
        int[] deg = new int[n];
        for (int i = 0; i < n - 1; i++) {
            int u = sc.nextInt()-1;
            int v = sc.nextInt()-1;
            adjj[u].add(v);
            adjj[v].add(u);
            Edge e = new Edge(u, v);
            adj[u].add(e);
            adj[v].add(e);
            deg[u]++;
            deg[v]++;
        }

        int[] queue = new int[n];
        int[] queue2 = new int[n];
        int qs2 = 0, qe2 = 0;
        int qs = 0, qe = 0;
        for (int i = 0; i < n; i++) {
            if(deg[i] == 1) {
                queue[qe++] = i;
                vis[i] = true;
            }
        }

        int[] size = new int[n];
        for (int i = 0; i < n; i++) {
            size[i] = adj[i].size();
        }
        boolean ok = true;
        for (int i = 0; i < k; i++) {
//            for (int j = qs; j < qe; j++) {
//                System.err.println(queue[j]+1);
//            }
//
//            System.err.println(ok);
//            System.err.println("------------------------");
            if(qs == qe)
            {
                ok = false;
                break;
            }
            while(qe>qs)
            {
                int u = queue[qs++];
                while(!adj[u].isEmpty()){
                    Edge e = adj[u].remove(adj[u].size()-1);
                    if(e.deleted)
                        continue;
                    int v = e.u==u?e.v:e.u;
                    if(!vis[v]){
                        if(i == k-1) {
                            if (size[v] < 3)
                                ok = false;
                        }else if(size[v] < 4) {
                            ok = false;
                        }
                        queue2[qe2++] = v;
                        vis[v] = true;
                    }

//                    adj[v].remove(u);
                    size[u]--;
                    e.deleted = true;
                    size[v]--;
                }
            }
            queue = queue2;
            qe = qe2;
            qs = qs2;
            qs2 = 0; qe2 = 0;
        }

        if(qe-qs != 1 || size[queue[qs]] != 0 )
            ok = false;
        for (int i = 0; i < n; i++) {
            if(!vis[i])
                ok = false;
        }
        if(!ok)
            pw.println("No");
        else
            if(check(queue[qs], -1, 0) == -1)
                pw.println("No");
            else
                pw.println("Yes");


        pw.flush();
        pw.close();
    }

    static class Edge{
        int u, v;
        boolean deleted;

        public Edge(int u, int v) {
            this.u = u;
            this.v = v;
            this.deleted = false;
        }
    }


    static class Scanner
    {
        StringTokenizer st; BufferedReader br;
        public Scanner(InputStream s){	br = new BufferedReader(new InputStreamReader(s));}
        public Scanner(java.lang.String s) throws FileNotFoundException {	br = new BufferedReader(new FileReader(new File(s)));}
        public java.lang.String next() throws IOException {while (st == null || !st.hasMoreTokens()) st = new StringTokenizer(br.readLine());return st.nextToken();}
        public int nextInt() throws IOException {return Integer.parseInt(next());}
        public long nextLong() throws IOException {return Long.parseLong(next());}
        public java.lang.String nextLine() throws IOException {return br.readLine();}
        public boolean ready() throws IOException {return br.ready();}
    }

}
