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.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.LinkedList;
import java.util.Queue;
import java.util.StringTokenizer;

public class P1067B
{
	static ArrayList<Integer>[] g;
	public static void main(String[] args)
	{
		FastScanner scan = new FastScanner();
		int n = scan.nextInt();
		g = new ArrayList[n];
		for (int i = 0; i < n; i++)
			g[i] = new ArrayList<>();
		int k = scan.nextInt();
		for (int i = 0; i < n-1; i++)
		{
			int u = scan.nextInt()-1;
			int v = scan.nextInt()-1;
			g[u].add(v);
			g[v].add(u);
		}
		Queue<Integer> q = new LinkedList<>();
		int[] level = new int[n];
		Arrays.fill(level, -1);
		for (int i = 0; i < n; i++)
		{
			if (g[i].size() == 1)
			{
				level[i] = 0;
				q.add(i);
			}
		}
		boolean valid = true;
		while (!q.isEmpty() && valid)
		{
			int p = q.poll();
			for (int i = 0; i < g[p].size(); i++)
			{
				int x = g[p].get(i);
				if (level[x] == -1)
				{
					level[x] = level[p]+1;
					q.add(x);
				}
				else if (level[x] >= level[p] && level[x] != level[p]+1)
					valid = false;
			}
		}
		if (!valid)
		{
			System.out.println("No");
			return;
		}
		//verify 3 or more
		int kcnt = 0;
		for (int i = 0; i < n; i++)
		{
			int deg = g[i].size();
			if (level[i] > k)
				valid = false;
			else if (level[i] == k)
			{
				kcnt++;
				if (deg < 3)
					valid = false;
			}
			else if (level[i] >= 1)
			{
				if (deg < 4)
					valid = false;
			}
		}
		if (kcnt != 1)
			valid = false;
		System.out.println(valid ? "Yes" : "No");
	}
	static class FastScanner
	{
		BufferedReader br;
		StringTokenizer st;

		public FastScanner()
		{
			try
			{
				br = new BufferedReader(new InputStreamReader(System.in));
				st = new StringTokenizer(br.readLine());
			} catch (Exception e)
			{
				e.printStackTrace();
			}
		}

		public String next()
		{
			if (st.hasMoreTokens())
				return st.nextToken();
			try
			{
				st = new StringTokenizer(br.readLine());
			} catch (Exception e)
			{
				e.printStackTrace();
			}
			return st.nextToken();
		}

		public int nextInt()
		{
			return Integer.parseInt(next());
		}

		public long nextLong()
		{
			return Long.parseLong(next());
		}

		public String nextLine()
		{
			String line = "";
			try
			{
				line = br.readLine();
			} catch (Exception e)
			{
				e.printStackTrace();
			}
			return line;
		}
	}
}
