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.ArrayDeque;
import java.util.ArrayList;
import java.util.Scanner;

public class Multiedgehog {

	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] ss = br.readLine().split(" ");
		int n = Integer.parseInt(ss[0]);
		int k = Integer.parseInt(ss[1]);
		ArrayList<ArrayList<Integer>> graph = new ArrayList<>();
		int[] degree = new int[n];
		for (int i = 0; i < n; i++) {
			graph.add(new ArrayList<>());
		}
		for (int i = 0; i < n - 1; i++) {
			String[] sv = br.readLine().split(" ");
			int a = Integer.parseInt(sv[0]) - 1;
			int b = Integer.parseInt(sv[1]) - 1;
			graph.get(a).add(b);
			graph.get(b).add(a);
			degree[a]++;
			degree[b]++;
		}
		boolean b = true;
		ArrayDeque<Integer> rs = new ArrayDeque<>();
		boolean[] visit = new boolean[n];
		for (int i = 0; i < n; i++) {

			if (degree[i] == 1) {
				rs.add(i);
                visit[i]=true;
			}
			if (degree[i] == 2) {
				b = false;
				break;
			}
		}
		if (!b) {
			System.out.println("NO");
			return;
		}
		int center = 0;


		while (rs.size() > 0) {
			int vs = rs.remove();
			center = vs;
			for (int x : graph.get(vs)) {
				if (!visit[x]) {
					rs.addLast(x);
					visit[x] = true;
				}
			}
		}
		boolean ans=dfs(center, -1, graph, degree, k);
		if(ans){
			System.out.println("YES");
		}else{
			System.out.println("NO");
		}
	}

	public static boolean dfs(int vert, int par, ArrayList<ArrayList<Integer>> graph, int[] degree, int k) {
		if(k==0){
			return degree[vert]==1;
		}
		int cnt=0;
		for (int v : graph.get(vert)) {
			if (par != v) {
			
				boolean bs=dfs(v, vert, graph, degree, k-1);
				cnt++;
				if(!bs){
					return false;
				}
			}
		}
		if(cnt>=3){
			return true;
		}
		return false;
	}
}
