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.*;
import java.math.*;
import java.util.*;

public class E {

	static ArrayList<Integer> adj[], adjList[];

	static int N, dp_down[][], dp_up[];
	static boolean[] visited;

	// Part 1
	static void dfs1(int u) {
		visited[u] = true;
		for (int i = 0; i < adjList[u].size(); ++i) {
			int v = adjList[u].get(i);
			if (!visited[v]) {
				dfs1(v);
				if (dp_down[v][0] + 1 > dp_down[u][1])
					dp_down[u][1] = dp_down[v][0] + 1;
				if (dp_down[u][1] > dp_down[u][0])
					swap(u);
			}
		}
	}

	static void dfs2(int u, int h) {
		visited[u] = true;
		dp_up[u] = h;
		for (int i = 0; i < adjList[u].size(); ++i) {
			int v = adjList[u].get(i);
			if (!visited[v]) {
				int h_nxt;
				if (dp_down[v][0] + 1 == dp_down[u][0])
					h_nxt = dp_down[u][1] + 1;
				else
					h_nxt = dp_down[u][0] + 1;
				dfs2(v, Math.max(h + 1, h_nxt));
			}
		}
	}

	static void swap(int u) {
		int x = dp_down[u][0], y = dp_down[u][1];
		dp_down[u][0] = y;
		dp_down[u][1] = x;
	}

	static void go() {
		dp_down = new int[N][2];
		dp_up = new int[N];
		visited = new boolean[N];
		dfs1(0);
		visited = new boolean[N];
		dfs2(0, 0);
	}

	// Part 2
	static int findRoot() {
		int[] deg = new int[N];
		Queue<Integer> q = new LinkedList<Integer>();
		for (int i = 0; i < N; ++i)
			if ((deg[i] = adjList[i].size()) == 1)
				q.add(i);
		int root = 0;
		while (!q.isEmpty()) {
			root = q.remove();
			for (int i = 0; i < adjList[root].size(); ++i) {
				int v = adjList[root].get(i);
				if (--deg[v] == 1)
					q.add(v);
			}
		}
		return root;

	}

	public static void main(String[] args) throws NumberFormatException, IOException {
		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);

		int n = sc.nextInt();
		N = n;
		int k = sc.nextInt();
		adj = new ArrayList[n];
		for (int i = 0; i < n; i++)
			adj[i] = new ArrayList<>();
		int m = n - 1;
		while (m-- > 0) {
			int u = sc.nextInt() - 1;
			int v = sc.nextInt() - 1;
			adj[v].add(u);
			adj[u].add(v);
		}
		adjList = adj;
		go();
		int root = findRoot();
		// System.out.println(u);
		visited = new boolean[n];
		dis = new int[n];
		// System.out.println(root);
		dfs(root, 0);
		int max = 0;
		for (int i = 0; i < n; i++)
			max = Math.max(max, dis[i]);
		if (max != k)
			pw.println("No");
		else {
			boolean ok = true;
			for (int i = 0; i < n; i++) {
				if (i == root) {
					if (adj[i].size() < 3)
						ok = false;
				} else if (adj[i].size() > 1) {
					if (adj[i].size() < 4)
						ok = false;
				} else if (dis[i] != k)
					ok = false;
			}
			pw.println(ok ? "Yes" : "No");
		}
		pw.flush();
	}

	static int[] dis;

	static void dfs(int u, int d) {
		visited[u] = true;
		dis[u] = d;
		for (int v : adj[u]) {
			if (!visited[v])
				dfs(v, d + 1);
		}

	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

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

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

		public String nextLine() throws IOException {
			return br.readLine();
		}

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

		public boolean ready() throws IOException {
			return br.ready();
		}
	}

}