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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.BufferedWriter;
import java.util.Collection;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.FileInputStream;
import java.util.ArrayList;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.Queue;
import java.util.LinkedList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        BMultihedgehog solver = new BMultihedgehog();
        solver.solve(1, in, out);
        out.close();
    }

    static class BMultihedgehog {
        private int n;
        private int k;
        private int maxDisFromCentre;
        private ArrayList<Integer>[] graph;
        private int[] dis;
        private int[] parent;
        private int maxDis;
        private int farthestVertex;

        private void bfs1(int start) {
            dis[start] = 0;
            maxDis = 0;
            farthestVertex = start;
            Queue<Integer> queue = new LinkedList<>();
            queue.offer(start);
            while (!queue.isEmpty()) {
                int v = queue.poll();
                for (int w : graph[v]) {
                    if (dis[w] == -1) {
                        queue.offer(w);
                        dis[w] = dis[v] + 1;
                        if (maxDis < dis[w]) {
                            maxDis = dis[w];
                            farthestVertex = w;
                        }
                    }
                }
            }

        }

        private void bfs2(int start) {
            dis[start] = 0;
            parent[start] = start;
            maxDis = 0;
            farthestVertex = start;
            Queue<Integer> queue = new LinkedList<>();
            queue.offer(start);
            while (!queue.isEmpty()) {
                int v = queue.poll();
                for (int w : graph[v]) {
                    if (dis[w] == -1) {
                        queue.offer(w);
                        dis[w] = dis[v] + 1;
                        parent[w] = v;
                        if (maxDis < dis[w]) {
                            maxDis = dis[w];
                            farthestVertex = w;
                        }
                    }
                }
            }
        }

        private boolean bfs3(int start) {
            dis[start] = 0;
            Queue<Integer> queue = new LinkedList<>();
            queue.offer(start);
            while (!queue.isEmpty()) {
                int v = queue.poll();
                for (int w : graph[v]) {
                    if (dis[w] == -1) {
                        dis[w] = dis[v] + 1;
                        queue.offer(w);
                        if (graph[w].size() == 1) {
                            if (dis[w] != maxDisFromCentre) {
                                return false;
                            }
                        } else if (graph[w].size() < 4) return false;
                    }
                }
            }
            return true;
        }

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            n = in.nextInt();
            k = in.nextInt();
            if (n <= 3) {
                out.println("No");
                out.flush();
                return;
            }
            graph = new ArrayList[n + 1];
            for (int i = 0; i <= n; i++) graph[i] = new ArrayList<>();
            dis = new int[n + 1];
            parent = new int[n + 1];
            for (int i = 0; i < n - 1; i++) {
                int u = in.nextInt(), v = in.nextInt();
                graph[u].add(v);
                graph[v].add(u);
            }
            Arrays.fill(dis, -1);
            bfs1(1);
            Arrays.fill(dis, -1);
            bfs2(farthestVertex);
            if (Util.isOdd(maxDis)) {
                out.println("No");
                out.flush();
                return;
            }
            int centre = farthestVertex;
            int currDis = maxDis;
            while (currDis > maxDis / 2) {
                centre = parent[centre];
                currDis = dis[centre];
            }
            maxDisFromCentre = maxDis - dis[centre];
            if (graph[centre].size() < 3 || maxDisFromCentre != k) {
                out.println("No");
                out.flush();
                return;
            }
            Arrays.fill(dis, -1);
            if (bfs3(centre)) out.println("Yes");
            else out.println("No");
            out.flush();
        }

    }

    static class Util {
        public static boolean isOdd(int num) {
            return ((num & 1) != 0);
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[8192];
        private int curChar;
        private int numChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public InputReader(FileInputStream file) {
            this.stream = file;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res = (res << 3) + (res << 1) + c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

    }

    static class OutputWriter {
        private final PrintWriter writer;
        private ArrayList<String> res = new ArrayList<>();
        private StringBuilder sb = new StringBuilder("");

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void println(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                sb.append(objects[i]);
            }
            res.add(sb.toString());
            sb = new StringBuilder("");
        }

        public void close() {
            writer.close();
        }

        public void flush() {
            for (String str : res) writer.printf("%s\n", str);
            res.clear();
            sb = new StringBuilder("");
        }

    }
}

