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.InputStream;
import java.io.InputStreamReader;
import java.util.*;

public class MainD {

    private FastScanner in;

    private void run() {
        in = new FastScanner(System.in);

        List<Set<Integer>> tree = new ArrayList<>();
        int n = in.nextInt();
        int k = in.nextInt();
        for (int i = 0; i < n; i++) {
            tree.add(new HashSet<>());
        }
        for (int i = 0; i < n - 1; i++) {
            int a = in.nextInt() - 1, b = in.nextInt() - 1;
            tree.get(a).add(b);
            tree.get(b).add(a);
        }


        System.out.println(isMulti(tree, k) ? "Yes" : "No");

    }

    private boolean isMulti(List<Set<Integer>> tree, int k) {
        Map<Integer, Set<Integer>> removed = new HashMap<>();
        for (int i = 0; i < tree.size(); i++) {
            if (tree.get(i) == null) {
                continue;
            }
            if (tree.get(i).size() == 1) {
                int nei = tree.get(i).stream().findAny().get();
                removed.computeIfAbsent(nei, key -> new HashSet<>()).add(i);
            }
        }
        if (removed.isEmpty()) {
            return false;
        }
        for (Map.Entry<Integer, Set<Integer>> entry : removed.entrySet()) {
            if (entry.getValue().size() < 3 || tree.get(entry.getKey()).size() > 1 + entry.getValue().size()) {
                return false;
            }
            for (Integer i: entry.getValue()) {
                tree.get(entry.getKey()).remove(i);
                tree.set(i, null);
            }
        }
        if (k == 1) {
            return removed.size() == 1 &&
                    tree.get(removed.keySet().stream().findAny().get()).size() == 0;
        } else {
            return isMulti(tree, k - 1);
        }
    }

    class FastScanner {

        BufferedReader br;
        StringTokenizer st;

        FastScanner(InputStream is) {
            br = new BufferedReader(new InputStreamReader(is));
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

    public static void main(String[] arg) {
        new MainD().run();
    }
}