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.security.*;
import java.text.*;
import java.util.*;
import java.util.concurrent.*;
import java.util.regex.*;

public class Solution {

    private static final Scanner sc = new Scanner(System.in);

    public static void main(String[] args) throws IOException {
        BufferedWriter bufferedWriter = new BufferedWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
        int n = sc.nextInt();
        int k = sc.nextInt();
        Node[] nodes = new Node[n];
        for (int i=0; i<n; ++i){
            nodes[i] = new Node();
        }
        for (int i=0; i<n-1; ++i){
            int f = sc.nextInt()-1;
            int t = sc.nextInt()-1;
            nodes[f].nbs.add(nodes[t]);
            nodes[t].nbs.add(nodes[f]);
        }
        Queue<Node> q = new LinkedList<>();
        int c3 = 0;
        for (int i=0; i<n; ++i) {
            if (nodes[i].nbs.size() == 1) {
                nodes[i].d = 0;
                q.add(nodes[i]);
            } else if (nodes[i].nbs.size() == 2){
                System.out.println("No");
                return;
            } else if (nodes[i].nbs.size() == 3){
                c3++;
                if (c3>1){
                    System.out.println("No");
                    return;
                }
            }
        }
        while(!q.isEmpty()){
            Node cur = q.remove();
            for (Node node : cur.nbs){
                if (node.d == Integer.MAX_VALUE){
                    node.d = cur.d + 1;
                    q.add(node);
                }
            }
        }
        Node center = null;
        for (int i=0; i<n; ++i){
            if (nodes[i].d == k){
                center = nodes[i];
                break;
            }
        }
        if (center == null){
            System.out.println("No");
            return;
        }
        if (c3 == 1){
            if (center.nbs.size() != 3){
                System.out.println("No");
                return;
            }
        }
        q.clear();
        center.visited = true;
        q.add(center);
        while(!q.isEmpty()){
            Node cur = q.remove();
            for (Node node : cur.nbs){
                if (!node.visited){
                    if (node.d != cur.d-1){
                        System.out.println("No");
                        return;
                    }
                    node.visited = true;
                    q.add(node);
                }
            }
        }
        System.out.println("Yes");
        bufferedWriter.close();
        sc.close();
    }

    public static class Node{
        boolean visited ;
        ArrayList<Node> nbs;
        int d;
        public Node(){
            visited = false;
            nbs = new ArrayList<>();
            d = Integer.MAX_VALUE;
        }
    }
}