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.*;

//find the center of the tree (delete leaves and keep doing that until there's one left)
//dfs from center to determine if it is k-hedgehog

public class multihedgehog {
	static int[] deg;
	static ArrayList<Integer>[] a;
	public static void main(String[] args) {
		Scanner scan=new Scanner(System.in);
		int n=scan.nextInt(), k=scan.nextInt();
		deg=new int[n];
		a=new ArrayList[n];
		for(int i=0;i<n;i++) a[i]=new ArrayList<>();
		for(int i=0;i<n-1;i++) {
			int u=scan.nextInt()-1, v=scan.nextInt()-1;
			a[u].add(v);
			a[v].add(u);
			deg[u]++;
			deg[v]++;
		}
		boolean[] v=new boolean[n];
		ArrayDeque<Integer> q=new ArrayDeque<>();
		for(int i=0;i<n;i++) {
			if(deg[i]==1) {
				q.offer(i);
				v[i]=true;
			}
		}
		int center=0;
		while(!q.isEmpty()) {
			int u=q.poll();
			center=u;
			for(int nxt:a[u]) {
				if(!v[nxt]) {
					q.offer(nxt);
					v[nxt]=true;
				}
			}
		}
		if(k(center,-1,k)) System.out.println("Yes");
		else System.out.println("No");
	}
	public static boolean k(int at, int prev, int k) {
		if(k==0) return deg[at]==1;
		int ct=0;
		for(int nxt:a[at]) {
			if(nxt==prev) continue;
			ct++;
			if(!k(nxt,at,k-1)) return false;
		}
		return ct>=3;
	}
}