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.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;

public class b {
	static ArrayList<Integer> adj[];
	public static void main(String[] args) throws IOException {
		FS  in = new FS();
		int n = in.nextInt();
		int k = in.nextInt();
		adj = new ArrayList[n];
		for(int i = 0; i < n; i++) 
			adj[i] = new ArrayList<>();
		for(int i = 0; i < n - 1; i++) {
			int u = in.nextInt()-1;
			int v = in.nextInt()-1;
			adj[u].add(v);
			adj[v].add(u);
		}
		dist = new int[n];
		dfs(0, -1, 0);
		int mx = 0;
		for(int i = 0; i < n; i++) {
			if(dist[mx] < dist[i]) 
				mx = i;
		}
		int mx2 = 0;
		dfs(mx, -1, 0);
		for(int i = 0; i < n; i++) {
			if(dist[mx2] < dist[i]) 
				mx2 = i;
		}
		
		int ld = dist[mx2];
		if(ld % 2 != 0) {
			System.out.println("No");
			return;
		}
		
		ArrayList<Integer> path = new ArrayList<>();
		path.add(mx);
		getPath(path, mx, -1, mx2);
		int center = path.get(ld/2);
		depth = new int[n];
		getDepth(center, -1);
		
		if(verify(center, k, -1)) {
			System.out.println("Yes");
		} else {
			System.out.println("No");
		}
		
	}
	static boolean verify(int u, int k,int p) {
		if(k == 0) {
			if(adj[u].size() == 1) return true;
			return false;
		}
		int sub = 1;
		if(p == -1) sub = 0;
		if(adj[u].size() - sub < 3) return false;
		for(int v : adj[u]) {
			if(v != p) {
				if(!verify(v, k-1, u)) return false;
			}
		}
		return true;
	}
	
	static void getDepth(int u,int p) {
		int ans = 1;
		for(int v : adj[u]) {
			if(v != p) {
				getDepth(v, u);
				ans = Math.max(ans, depth[v] + 1);
			}
		}
		depth[u] = ans;
	}
	static int depth[];
	static int dist[];
	static boolean getPath(ArrayList<Integer> path, int u,int p, int g) {
		if(u == g) return true;
		for(int v : adj[u]) {
			if(v != p) {
				path.add(v);
				if(getPath(path, v, u, g)) return true;
				path.remove(path.size()-1);
			}
		}
		return false;
	}
	static void dfs(int u, int p, int d) {
		dist[u] = d;
		for(int v : adj[u]) {
			if(v != p) {
				dfs(v, u, d + 1);
			}
		}
	}
	
	static class FS {
		BufferedReader  br;
		StringTokenizer st;
		FS() {
			br = new BufferedReader(new InputStreamReader(System.in));
			st = new StringTokenizer("");
		}
		
		String next() throws IOException {
			if(!st.hasMoreElements())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
		
		Integer nextInt() throws IOException {
			return Integer.parseInt(next());
			
		}
	}
}
