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.

import java.math.BigInteger;
import java.text.DecimalFormat;
import java.util.*;
import java.io.*;



public class Main {
    private static int n,K;
    private static HashSet<Integer> [] G,hG;
    private static int [] deg;
    private static void read(IO io) throws IOException{
        n = io.getNextInt();
        K = io.getNextInt();
        G = new HashSet[n+1];
        for (int i = 0;i <= n;i++)
            G[i] = new HashSet<>();
        for (int e = 1;e < n;e++) {
            int a = io.getNextInt(),b = io.getNextInt();
            G[a].add(b);
            G[b].add(a);
        }
    }
    private static int getRoot(){
        Queue<Integer> q = new LinkedList<>();
        int u = 0;
        hG = new HashSet[n+1];
        for (int i = 1;i <= n;i++) {
            hG[i] = new HashSet<>(G[i]);
            if (hG[i].size() == 1)
                q.add(i);
        }
        while (!q.isEmpty()) {
            u = q.poll();
            for (int v : hG[u]) {
                hG[v].remove(u);
                if (hG[v].size() == 1)
                    q.add(v);
            }
        }
        return u;
    }
    private static boolean dfs(int u,int p,int k){
        if (k > K) return false;
        boolean ret = true;
        int ctr = 0;
        for (int v : G[u])
            if (v != p) {
                ret &= dfs(v, u, k + 1);
                ctr++;
            }
        if (k == K) ret &= ctr == 0;
        else ret &= ctr >= 3;
        return ret;
    }
    private static boolean solve(){
        if (n < 4) return false;
        int root = getRoot();
        if (root == 0) return false;
        return dfs(root,0,0);
    }
    public static void main(String[] args) throws Exception {
        IO io ;
        try {
            io = new IO("in.in", null);
        } catch (IOException e) {
            io = new IO(null, null);
        }
        read(io);
        io.println(solve() ? "Yes" : "No");
        io.close();
    }
    private static final int onebillion7 = 1000000007;
}


class IO{
    private BufferedReader br;
    private StringTokenizer st;
    private PrintWriter writer;
    private String inputFile,outputFile;

    public boolean hasMore() throws IOException{
        if(st != null && st.hasMoreTokens()) return true;
        if(br != null && br.ready()) return true;
        return false;
    }

    public String getNext() throws FileNotFoundException, IOException{
        while(st == null || !st.hasMoreTokens()) st = new StringTokenizer(br.readLine());
        return st.nextToken();
    }

    public String getNextLine() throws FileNotFoundException, IOException{
        return br.readLine().trim();
    }

    public int getNextInt() throws FileNotFoundException, IOException{
        return Integer.parseInt(getNext());
    }
    public long getNextLong() throws FileNotFoundException, IOException{
        return Long.parseLong(getNext());
    }

    public void print(double x,int num_digits) throws  IOException{
        writer.printf("%." + num_digits + "f" ,x);
    }
    public void println(double x,int num_digits) throws  IOException{
        writer.printf("%." + num_digits + "f\n" ,x);
    }
    public void print(Object o) throws  IOException{
        writer.print(o.toString());
    }

    public void println(Object o) throws  IOException{
        writer.println(o.toString());
    }
    public IO(String x,String y) throws FileNotFoundException, IOException{
        inputFile = x;
        outputFile = y;
        if(x != null) br = new BufferedReader(new FileReader(inputFile));
        else br = new BufferedReader(new InputStreamReader(System.in));
        if(y != null) writer = new PrintWriter(new BufferedWriter(new FileWriter(outputFile)));
        else writer = new PrintWriter(new OutputStreamWriter(System.out));
    }

    protected void close() throws IOException{
        br.close();
        writer.close();
    }
    public void outputArr(Object [] A) throws IOException{
        int L = A.length;
        for (int i = 0;i < L;i++) {
            if(i > 0) writer.print(" ");
            writer.print(A[i]);
        }
        writer.print("\n");
    }
}