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.*;
import java.util.*;

public class Solution{
	InputStream is;
	static PrintWriter out;
	String INPUT = "";
	static long mod = (long)1e9+7L;
	
	int n, k;
	ArrayList<Integer>[] adj;
	int[] next;
	int centre = -1;
	public void solve(){
		n = ni(); k = ni();
		adj = new ArrayList[n+1];
		for(int i = 0; i <= n; i++){
			adj[i] = new ArrayList<Integer>();
		}

		for(int i = 0; i < n-1; i++){
			int x = ni(), y = ni();
			adj[x].add(y);
			adj[y].add(x);
		}

		next = new int[n+1];
		boolean[] in = new boolean[n+1], vis = new boolean[n+1];
		int depth = 1, lvls =0;
		LinkedList<Integer> Q = new LinkedList<Integer>();
		for(int i = 1; i <= n; i++){
			if(adj[i].size() == 1){
				Q.add(i);
				in[i] = true;
				lvls += 1;
			}
		}
		Q.add(-1);
		int visct = 0;
		while(Q.size() > 1){
			//out.println(Q);
			int u = Q.poll();
			if(u == -1){
				lvls = 0;
				Q.add(u);
				depth += 1;
				continue;
			}
			if(vis[u])continue;
			vis[u] = true;
			visct += 1;
			lvls += 1;
			int degree = 0;
			for(int v : adj[u]){
				if(!vis[v]){
					degree += 1;
					if(!in[v]){
						Q.add(v);
						in[v] = true;
					}
				}
			}
			if(adj[u].size() == 1)continue;

			if(degree == 0 && (adj[u].size() < 3 || lvls > 1) ){
				out.println("No");
				return;
			}
			else if(degree == 0){
				centre = u;
				break;
			}

			if(degree > 1 || (adj[u].size()-1) < 3){
				out.println("No");
				return;
			}

		}
//out.println(centre);
//out.println(depth);
		if((depth-1) != k || centre == -1){
			out.println("No");
			return;
		}

		if(visct == n)
			out.println("Yes");
		else
			out.println("No");
	}

	void run(){
		is = new DataInputStream(System.in);
		out = new PrintWriter(System.out);
		int t=1;while(t-->0)solve();
		out.flush();
	}
	public static void main(String[] args)throws Exception{new Solution().run();}
	long mod(long v, long m){if(v<0){long q=(Math.abs(v)+m-1L)/m;v=v+q*m;}return v%m;}
    long mod(long v){if(v<0){long q=(Math.abs(v)+mod-1L)/mod;v=v+q*mod;}return v%mod;}
	//Fast I/O code is copied from uwi code.
	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();
		}
	}
	static  int i(long x){return (int)Math.round(x);}
	static class Pair implements Comparable<Pair>{
		long fs,sc;
		Pair(long a,long b){
			fs=a;sc=b;
		}
		public int compareTo(Pair p){
			if(this.fs>p.fs)return 1;
			else if(this.fs<p.fs)return -1;
			else{
				return i(this.sc-p.sc);
			}
			//return i(this.sc-p.sc);
		}
		public String toString(){
			return "("+fs+","+sc+")";
		}	
	}
	
}