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

public class E {
    public static void main(String[] args) throws IOException {
        try (Input input = new StandardInput(); PrintWriter writer = new PrintWriter(System.out)) {
            int n = input.nextInt(), k = input.nextInt();
            if (n < 4) {
                writer.println("No");
                return;
            }
            List[] g = new List[n + 1];
            for (int i = 1; i <= n; i++) {
                g[i] = new ArrayList<Integer>(4);
            }
            int[] c = new int[n + 1];
            int[] d = new int[n + 1];
            int[] q = new int[n + 1];
            int head = 0;
            int tail = 0;
            for (int i = 1; i < n; i++) {
                int a = input.nextInt();
                int b = input.nextInt();
                g[a].add(b);
                g[b].add(a);
                c[a]++;
                c[b]++;
            }
            Arrays.fill(d, -1);
            for (int i = 1; i <= n; i++) {
                if (c[i] == 1) {
                    q[tail++] = i;
                    d[i] = 0;
                }
            }
            while(head < tail) {
                int u = q[head++];
                for (int v: (List<Integer>)g[u]) {
                    if (d[v] == -1) {
                        d[v] = d[u] + 1;
                        q[tail++] = v;
                    } else if (d[v] == d[u] + 1 || d[v] == d[u] - 1) {
                    } else {
                        writer.println("No");
                        return;
                    }
                }
            }
            if (d[q[head - 1]] != k) {
                writer.println("No");
                return;
            }
            if (d[q[head - 1]] == d[q[head - 2]]) {
                writer.println("No");
                return;
            }
            for (int i = 1; i <= n; i++) {
                if (d[i] > 0) {
                    if (d[i] == k && g[i].size() < 3) {
                        writer.println("No");
                        return;
                    }
                    if (d[i] != k && g[i].size() < 4) {
                        writer.println("No");
                        return;
                    }
                }
            }
            writer.println("Yes");
        }
    }

    interface Input extends Closeable {
        String next() throws IOException;

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

        default long nextLong() throws IOException {
            return Long.parseLong(next());
        }
    }

    private static class StandardInput implements Input {
        private final BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));

        private StringTokenizer stringTokenizer;

        @Override
        public void close() throws IOException {
            reader.close();
        }

        @Override
        public String next() throws IOException {
            if (stringTokenizer == null || !stringTokenizer.hasMoreTokens()) {
                stringTokenizer = new StringTokenizer(reader.readLine());
            }
            return stringTokenizer.nextToken();
        }
    }
}