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.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;

public class B {
	static PrintWriter out = new PrintWriter(System.out);

	static int N, K;
	static ArrayList<Integer> adj[];
	public static void main(String[] args) {
		FS in = new FS();
		N = in.nextInt();
		K = in.nextInt();
		adj = new ArrayList[N];
		for(int i = 0; i < N; i++) adj[i] = new ArrayList<Integer>();
		
		for(int i = 0; i < N-1; i++) {
			int a = in.nextInt()-1;
			int b = in.nextInt()-1;
			adj[a].add(b);
			adj[b].add(a);
		}
		
		int d1[] = getDist(0);
		int m = 0;
		for(int i = 1; i < N; i++) if(d1[i] > d1[m]) m = i;
		int d2[] = getDist(m);
		
		int max = 0;
		for(int ii : d2) if(ii > max) max = ii;
			

		// get max dist

		
		boolean good = true;
		if(max%2 != 0) good = false;
		else {
			int m2 = 0;
			for(int i = 1; i < N; i++) if(d2[i] > d2[m2]) m2 = i;
			int d3[] = getDist(m2);
			
			int dToRoot = max/2;
			int root = -1;
			for(int i = 0; i < N; i++) {
				if(d2[i] == dToRoot && d3[i] == dToRoot) {
					if(root != -1) good = false;
					root = i;
				}
			}
			good &= dfs(root, -1, K);
		}
		
		out.println(good ? "Yes":"No");
		out.close();
	}
	
	static boolean dfs(int node, int p, int k) {
		if(adj[node].size() == 1) {
			//is leaf
			return k == 0 && p != -1;
		}
		if(k == 0) return false;
		
		int sz = adj[node].size();
		if(p != -1) sz--;
		
		
		if(sz < 3) return false;
		
		boolean res = true;
		for(int ii : adj[node]) {
			if(ii != p) res &= dfs(ii, node, k-1);
		}
		return res;
	}
	
	static int[] getDist(int st) {
		int d[] = new int[N];
		Arrays.fill(d, -1);
		d[st] = 0;
		ArrayDeque<Integer> q = new ArrayDeque<Integer>();
		q.add(st);
		while(!q.isEmpty()) {
			int v = q.poll();
			for(int ii : adj[v]) {
				if(d[ii] != -1) continue;
				d[ii] = d[v]+1;
				q.add(ii);
			}
		}
		return d;
	}
	
	static class FS{
		BufferedReader br;
		StringTokenizer st;
		public FS() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}
		String next() {
			while(st == null || !st.hasMoreElements()) {
				try {st = new StringTokenizer(br.readLine());}
				catch(Exception e) { throw null;}
			}
			return st.nextToken();
		}
		int nextInt() { return Integer.parseInt(next());}
		double nextDouble() { return Double.parseDouble(next());}
		long nextLong() { return Long.parseLong(next());}
		int[] NIA(int n) {
			int r[] = new int[n];
			for(int i = 0; i < n; i++) r[i] = nextInt();
			return r;
		}
		long[] NLA(int n) {
			long r[] = new long[n];
			for(int i = 0; i < n; i++) r[i] = nextLong();
			return r;
		}
		char[][] grid(int r, int c){
			char res[][] = new char[r][c];
			for(int i = 0; i < r; i++) {
				char l[] = next().toCharArray();
				for(int j = 0; j < c; j++) {
					res[i][j] = l[j];
				}
			}
			return res;
		}
	}
	
}
