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.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;

public class B {

	public static void main(String[] args) throws IOException {
		// TODO Auto-generated method stub
		FastScanner in = new FastScanner(System.in);
		int n = in.nextInt();
		int k = in.nextInt();
		if (n < 4) {
			System.out.println("No");
			return;
		}
		ArrayList<Integer>[] graph = new ArrayList[n];
		for (int i = 0; i < n; i++) {
			graph[i] = new ArrayList<Integer>();
		}

		for (int i = 0; i < n - 1; i++) {
			int u = in.nextInt() - 1;
			int v = in.nextInt() - 1;
			graph[u].add(v);
			graph[v].add(u);
		}

		int firstleaf = 0;
		for (int i = 0; i < n; i++) {
			if (graph[i].size() == 1) {
				firstleaf = i;
				break;
			}
		}
		int[] dist = new int[n];
		Arrays.fill(dist, Integer.MAX_VALUE / 3);
		dist[firstleaf] = 0;
		ArrayDeque<Integer> q = new ArrayDeque<Integer>();
		q.add(firstleaf);
		while (!q.isEmpty()) {
			int cur = q.poll();
			for (Integer e : graph[cur]) {
				if (dist[e] > dist[cur] + 1) {
					dist[e] = dist[cur] + 1;
					q.add(e);
				}
			}
		}
		int furthest = 0;
		int furthestnode = 0;
		for (int i = 0; i < dist.length; i++) {
			furthest = Math.max(furthest, dist[i]);
			if (dist[i] >= furthest)
				furthestnode = i;
		}
		// System.out.println(furthest);
		if (furthest % 2 != 0) {
			System.out.println("No");
			// System.err.println(1);
			return;
		}
		int[] dist2 = new int[n];
		Arrays.fill(dist2, Integer.MAX_VALUE / 3);
		dist2[furthestnode] = 0;
		q = new ArrayDeque<Integer>();
		q.add(furthestnode);
		while (!q.isEmpty()) {
			int cur = q.poll();
			for (Integer e : graph[cur]) {
				if (dist2[e] > dist2[cur] + 1) {
					dist2[e] = dist2[cur] + 1;
					q.add(e);
				}
			}
		}
		int middledist = furthest / 2;
		int center = -1;
		for (int i = 0; i < dist.length; i++) {
			if (dist[i] == middledist && dist2[i] == middledist) {
				center = i;
			}
		}
		if (center == -1) {
			System.out.println("No");
			return;
		}
		// System.out.println(center);
		dist = new int[n];
		Arrays.fill(dist, Integer.MAX_VALUE / 3);
		dist[center] = 0;
		q = new ArrayDeque<Integer>();
		q.add(center);
		while (!q.isEmpty()) {
			int cur = q.poll();
			for (Integer e : graph[cur]) {
				if (dist[e] > dist[cur] + 1) {
					dist[e] = dist[cur] + 1;
					q.add(e);
				}
			}
		}
		// System.out.println(center);
		if (graph[center].size() < 3) {
			System.out.println("No");
			// System.err.println(2);
			return;
		}
		int leafdist = 0;
		for (int i = 0; i < dist.length; i++)
			leafdist = Math.max(dist[i], leafdist);
		if (leafdist != k) {
			System.out.println("No");
			// System.err.println(3);
			return;
		}
		for (int i = 0; i < dist.length; i++) {
			if (i == center)
				continue;
			if (graph[i].size() == 1) {
				if (dist[i] != leafdist) {
					System.out.println("No");
					// System.err.println(4);
					return;
				}
				continue;
			}
			if (dist[i] == leafdist) {
				if (graph[i].size() != 1) {
					System.out.println("No");
					// System.err.println(5);
					return;
				}
			}
			if (graph[i].size() < 4) {
				System.out.println("No");
				// System.err.println(6);
				return;
			}
		}
		System.out.println("Yes");
	}

	static class FastScanner {
		BufferedReader br;
		StringTokenizer st;

		public FastScanner(InputStream i) {
			br = new BufferedReader(new InputStreamReader(i));
			st = new StringTokenizer("");
		}

		public String next() throws IOException {
			if (st.hasMoreTokens())
				return st.nextToken();
			else
				st = new StringTokenizer(br.readLine());
			return next();
		}

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

		// #
		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}
		// $
	}

}
