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.util.*;
import java.io.*;
 
public class Main {
	public static void main(String args[]) {new Main().work();}
	
	Scanner in = new Scanner(System.in);
	PrintWriter out = new PrintWriter(System.out);
	void work() {		
		int n=in.nextInt();
	    int k=in.nextInt();
	    ArrayList<Integer>[] graph=(ArrayList<Integer>[])new ArrayList[n];
	    int[] degree=new int[n];
	    for(int i=0;i<n;i++) graph[i]=new ArrayList<>();
	    for(int i=1;i<=n-1;i++){
	        int e1=in.nextInt()-1;
	        int e2=in.nextInt()-1;
	        graph[e1].add(e2);
	        graph[e2].add(e1);
	        degree[e1]++;
	        degree[e2]++;
	    }
	    LinkedList<Integer> queue=new LinkedList<>();
	    for(int i=0;i<n;i++){
	        if(degree[i]==1){
	            queue.add(i);
	        }
	    }
	    while(queue.size()>1&&k>0){
	        int len=queue.size();
	        HashSet<Integer> set=new HashSet<>();
	        int cnt=0;//check degree
	        int[] rec=new int[n];
	        while(len-->0){
	            int node=queue.poll();
	            degree[node]--;
	            for(int nn:graph[node]){
	                if(degree[nn]>0){
	                    rec[nn]++;
	                    if(rec[nn]==1) cnt++;
	                    if(rec[nn]==3) cnt--;
	                    degree[nn]--;
	                    set.add(nn);
	                }
	                if(degree[nn]==1){
	                    queue.add(nn);
	                }
	            } 
	        }
	        if(cnt>0||set.size()!=queue.size()){
	            out.print("No");
	            out.flush();
	            return;
	        }
	        k--;
	    }
	    if(queue.size()==1&&k==0){
	        out.print("Yes");
	    }else{
	        out.print("No");
	    }
	    out.flush();
	}
}
