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.BufferedInputStream;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.ArrayList;

public class E {
	
	public void solve(JS in, PrintWriter out) {
		int n = in.nextInt();
		int k = in.nextInt();
		ArrayList<Integer>[] vs = new ArrayList[n];
		for(int i = 0; i < n; ++i) vs[i] = new ArrayList<>();
		for(int i = 0; i < n - 1; ++i) {
			int u = in.nextInt() - 1;
			int v = in.nextInt() - 1;
			vs[u].add(v); vs[v].add(u);
		}
		boolean possible = true;
		ArrayDeque<Integer> q = new ArrayDeque<>();
		boolean[] visited = new boolean[n];
		for(int i = 0; i < n; ++i)  {
			if(vs[i].size() == 1) {
				q.add(i);
				visited[i] = true;
			} else if(vs[i].size() == 2) {
				possible = false;
				break;
			}
		}
		if(!possible) {
			out.println("No");
			return;
		}
		int[] dist = new int[n];
		int maxDist = 0;
		while(!q.isEmpty()) {
			int node = q.pollFirst();
			for(int i : vs[node]) {
				if(!visited[i]) {
					visited[i] = true;
					dist[i] = dist[node] + 1;
					maxDist = Math.max(maxDist, dist[i]);
					q.add(i);
				} else if(dist[i] > dist[node] && dist[i] != dist[node] + 1) {
					possible = false;
//					System.out.println("this node: " + (i + 1));
				}
			}
		}
		int cnt = 0;
		int center = -1;
		for(int i = 0; i < n; ++i) {
			if(dist[i] == maxDist) {
				++cnt;
				center = i;
			}
			else if(vs[i].size() != 1 && vs[i].size() < 4) {
				possible = false;
//				System.out.println("not possible: " + (i + 1) + " with degree " + vs[i].size());
			}
		}
				
		if(cnt > 1 || maxDist != k || !possible) {
			out.println("No");
			return;
		}
		
		visited = new boolean[n];
		q = new ArrayDeque<>();
		dist = new int[n];
		visited[center] = true; q.add(center);
		
		while(!q.isEmpty()) {
			int node = q.pollFirst();
			for(int i : vs[node]) if(!visited[i]) {
				dist[i] = dist[node] + 1;
				visited[i] = true;
				q.add(i);
			}
		}
		for(int i = 0; i < n; ++i) {
			if(vs[i].size() == 1 && dist[i] != k) possible = false;
			if(i != center && vs[i].size() != 1 && vs[i].size() < 4) possible = false;
		}
		out.println(possible ? "Yes" : "No");
	}
	
	public static void main(String[] args) {
		JS in = new JS();
		PrintWriter out = new PrintWriter(System.out);
		new E().solve(in, out);
		out.close();
	}
	
	static class JS {
		public int BS = 1<<16;
		public char NC = (char)0;
		byte[] buf = new byte[BS];
		int bId = 0, size = 0;
		char c = NC;
		double num = 1;
		BufferedInputStream in;

		public JS() {
			in = new BufferedInputStream(System.in, BS);
		}

		public JS(String s) throws FileNotFoundException {
			in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
		}

		public char nextChar(){
			while(bId==size) {
				try {
					size = in.read(buf);
				}catch(Exception e) {
					return NC;
				}
				if(size==-1)return NC;
				bId=0;
			}
			return (char)buf[bId++];
		}

		public int nextInt() {
			return (int)nextLong();
		}

		public long nextLong() {
			num=1;
			boolean neg = false;
			if(c==NC)c=nextChar();
			for(;(c<'0' || c>'9'); c = nextChar()) {
				if(c=='-')neg=true;
			}
			long res = 0;
			for(; c>='0' && c <='9'; c=nextChar()) {
				res = (res<<3)+(res<<1)+c-'0';
				num*=10;
			}
			return neg?-res:res;
		}

		public double nextDouble() {
			double cur = nextLong();
			return c!='.' ? cur:cur+nextLong()/num;
		}

		public String next() {
			StringBuilder res = new StringBuilder();
			while(c<=32)c=nextChar();
			while(c>32) {
				res.append(c);
				c=nextChar();
			}
			return res.toString();
		}

		public String nextLine() {
			StringBuilder res = new StringBuilder();
			while(c<=32)c=nextChar();
			while(c!='\n') {
				res.append(c);
				c=nextChar();
			}
			return res.toString();
		}

		public boolean hasNext() {
			if(c>32)return true;
			while(true) {
				c=nextChar();
				if(c==NC)return false;
				else if(c>32)return true;
			}
		}
	}
}
