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.io.BufferedReader;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.io.UnsupportedEncodingException;
import java.util.LinkedList;
import java.util.StringTokenizer;

public class Main {
    
    static Vertex l, cntr, d;
    static int max;
    
    public static void main(String[] args) throws UnsupportedEncodingException, IOException, Exception {
        Reader.init(System.in);
        StringBuilder out = new StringBuilder();
        int n = Reader.nextInt();
        long k = Reader.nextLong();
        Graph g = new Graph(n);
        while(n-- > 1)
            g.addEdge(Reader.nextInt(), Reader.nextInt());
        dfs(g.v[1], null);
        l.lvl = 1;
        calcLvl(l, null);
        if((max & 1) == 0) {
            System.out.println("No");
            return;
        }
        max = max / 2 + 1;
        getCntr(l, null);
        out.append(calc(cntr, null, k) ? "Yes\n" : "No\n");
        PrintWriter pw = new PrintWriter(System.out);
        pw.print(out);
        pw.close();
    }
    
    static boolean calc(Vertex v, Vertex p, long k) {
        if((k == 0l && v.edges.size() > 1) || (k > 0l && ((v != cntr && v.edges.size() < 4) || (v == cntr && v.edges.size() < 3))))
            return false;
        for(Vertex c : v.edges)
            if(c != p && !calc(c, v, k - 1l))
                return false;
        return true;
    }
    
    static boolean getCntr(Vertex v, Vertex p) {
        if(d == v) {
            if(v.lvl == max)
                cntr = v;
            return true;
        }
        for(Vertex c : v.edges)
            if(c != p && getCntr(c, v)) {
                if(v.lvl == max)
                    cntr = v;
                return true;
            }
        return false;
    }
    
    static void dfs(Vertex v, Vertex p) {
        l = v;
        for(Vertex c : v.edges)
            if(c != p)
                dfs(c, v);
    }
    
    static void calcLvl(Vertex v, Vertex p) {
        if(max < v.lvl) {
            max = v.lvl;
            d = v;
        }
        for(Vertex c : v.edges)
            if(c != p) {
                c.lvl = v.lvl + 1;
                calcLvl(c, v);
            }
    }

}

class Vertex {
    
    int name, lvl;
    LinkedList<Vertex> edges;
    
    public Vertex(int n) {
        name = n;
        edges = new LinkedList<Vertex>();
    }
    
}

class Graph {
    
    Vertex[] v;
    
    public Graph(int s) {
        v = new Vertex[s + 1];
        for(int i = 1; i <= s; i++)
            v[i] = new Vertex(i);
    }
    
    public void addEdge(int v1, int v2) {
        v[v1].edges.add(v[v2]);
        v[v2].edges.add(v[v1]);
    }
    
}

class Reader {

    static BufferedReader reader;
    static StringTokenizer tokenizer;

    static void init(InputStream input) throws UnsupportedEncodingException {
        reader = new BufferedReader(
                new InputStreamReader(input, "UTF-8"));
        tokenizer = new StringTokenizer("");
    }

    static void init(String url) throws FileNotFoundException {
        reader = new BufferedReader(new FileReader(url));
        tokenizer = new StringTokenizer("");
    }

    static String next() throws IOException {
        while (!tokenizer.hasMoreTokens()) {
            //TODO add check for eof if necessary
            tokenizer = new StringTokenizer(
                    reader.readLine());
        }
        return tokenizer.nextToken();
    }

    static String nextLine() throws IOException {
        return reader.readLine();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    static double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }

    static long nextLong() throws IOException {
        return Long.parseLong(next());
    }
}