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 ;
import java.io.*;
import java.util.*;

public class Problem_1068E
{
	static ArrayList<Integer> adjList[],adj[];
	static boolean visited[];
	public static void main(String[] args) throws IOException 
	{
		Scanner sc = new Scanner();
		PrintWriter pw = new PrintWriter(System.out);
		int n=sc.nextInt(),k=sc.nextInt();
		if(n==1)
		{
			System.out.println("NO");
			return;
		}
		adjList=new ArrayList[n];
		deg=new int[n];
		p=new int[n];
		visited=new boolean[n];
		map=new HashMap<>();
		for(int i=0;i<n;i++)adjList[i]=new ArrayList<>();
		for(int i=1;i<n;i++)
		{
			int u=sc.nextInt()-1,v=sc.nextInt()-1;
			adjList[u].add(v);
			adjList[v].add(u);
		}
		p2=new int[n];
		int length=dfs(0,1,0);
		int x=map.get(length);
		visited=new boolean[n];
		map=new HashMap<>();
		p2=new int[n];
		length=dfs(x,1,x);
		int y=map.get(length);
//		System.out.println(map);
		if(length%2==0)
		{			
			System.out.println("NO");
			return;
		}
//		int mid=length/2 + 1;
//		int mid_nod=map.get(mid);
//		System.out.println(mid_nod);
		int mid_nod=getmid(y,length);
		Queue<Integer>q=new LinkedList<>();
		Queue<Integer>level=new LinkedList<>();
		q.add(mid_nod);
		level.add(k);
		while(!q.isEmpty())
		{
			int cur=q.poll(),lev=level.poll();
			if(lev>0 && adjList[cur].size()<4 && cur!=mid_nod)
			{			
				System.out.println("no");
				return;
			}
			if(cur==mid_nod && adjList[cur].size()<3)
			{
				System.out.println("No");
				return;
			}
			if(lev==0)
			{	if( adjList[cur].size()==1)
					continue;
				else 
				{
					System.out.println("no");
					return;
				}
			}
			for(int nxt:adjList[cur])
				if(nxt!=p[cur])
				{
					p[nxt]=cur;
					q.add(nxt);
					level.add(lev-1);
				}
		}
		pw.print("YES");
		pw.close();    
	}
	static int getmid(int last,int length)
	{
		int count=0;
		while(true)
		{
			last=p2[last];
			count++;
			if(count==length/2)
				return last;
		}
	}
	static int[] deg,p,p2;
	static HashMap<Integer, Integer>map;
	public static int dfs(int n,int d,int parent)
	{
		p2[n]=parent;
		visited[n]=true;
		if(!map.containsKey(d))
			map.put(d,n);
		int max=0;
		for(int v:adjList[n])
			if(!visited[v])
				max=Math.max(max,dfs(v,d+1,n));
		return max+1;
	}
//	static boolean dfs(int n,int l)
//	{
//		
//	}
	static class Scanner {
		BufferedReader br;
		StringTokenizer st;
		
		Scanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}
		
		String next() throws IOException {
			while (st == null || !st.hasMoreTokens()) {
				st = new StringTokenizer(br.readLine());
			}
			return st.nextToken();
		}
		
		int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
		
		long nextLong() throws IOException {
			return Long.parseLong(next());
		}
		
		double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}
		
		String nextLine() throws IOException {
			return br.readLine();
		}
		boolean hasnext() throws IOException{
			return br.ready();
		}
		
	}
}
