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.IOException;
import java.io.InputStream;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashSet;
import java.util.InputMismatchException;

public class P1068E
{
	@SuppressWarnings("unchecked")
	public static void main(String[] args)
	{
		FastScanner in = new FastScanner(System.in);
		int n = in.nextInt();
		int k = in.nextInt();
		ArrayList<Integer>[] edges = new ArrayList[n];
		for (int i = 0; i < n; i++)
			edges[i] = new ArrayList<>();
		for (int i = 0; i < n - 1; i++) {
			int u = in.nextInt() - 1;
			int v = in.nextInt() - 1;
			edges[u].add(v);
			edges[v].add(u);
		}
		HashSet<Integer> bfs = new HashSet<>();
		boolean[] seen = new boolean[n];
		int[] dists = new int[n];
		Arrays.fill(dists, -1);
		for (int i = 0; i < n; i++) {
			if (edges[i].size() == 1) {
				bfs.add(i);
				dists[i] = 0;
			}
		}
		int[] parents = new int[n];
		Arrays.fill(parents, -1);
		while (!bfs.isEmpty()) {
			for (int i : bfs)
				seen[i] = true;
			HashSet<Integer> pass = new HashSet<>();
			for (int i : bfs) {
				if (parents[i] != -1)
					continue;
				for (int v : edges[i]) {
					if (parents[v] == -1 && !seen[v]) {
						parents[i] = v;
						dists[v] = dists[i] + 1;
						pass.add(v);
						break;
					}
				}
			}
			bfs = pass;
		}
		ArrayList<Integer> roots = new ArrayList<>();
		for (int i = 0; i < n; i++)
			if (parents[i] == -1)
				roots.add(i);
		if (roots.size() != 1) {
			System.out.println("No");
			System.exit(0);
		}
		int root = roots.get(0);
		if (dists[root] != k) {
			System.out.println("No");
			System.exit(0);
		}
		for (int i = 0; i < n; i++) {
			if (edges[i].size() == 1)
				continue;
			if (i != root && edges[i].size() < 4) {
				System.out.println("No");
				System.exit(0);
			}
			if (i == root && edges[i].size() < 3) {
				System.out.println("No");
				System.exit(0);
			}
		}
		System.out.println("Yes");
	}
	
	/**
	 * Source: Matt Fontaine
	 */
	public static class FastScanner
	{
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;

		public FastScanner(InputStream stream)
		{
			this.stream = stream;
		}

		int read()
		{
			if (numChars == -1)
				throw new InputMismatchException();
			if (curChar >= numChars)
			{
				curChar = 0;
				try
				{
					numChars = stream.read(buf);
				} catch (IOException e)
				{
					throw new InputMismatchException();
				}
				if (numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		boolean isSpaceChar(int c)
		{
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		boolean isEndline(int c)
		{
			return c == '\n' || c == '\r' || c == -1;
		}

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

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

		public double nextDouble()
		{
			return Double.parseDouble(next());
		}

		public String next()
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do
			{
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		public String nextLine()
		{
			int c = read();
			while (isEndline(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do
			{
				res.appendCodePoint(c);
				c = read();
			} while (!isEndline(c));
			return res.toString();
		}
	}
}