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.BigInteger;
import java.util.*;

public class B {
    public static void main(String[] args) throws Throwable {
        MyScanner sc = new MyScanner();
        PrintWriter pw = new PrintWriter(System.out);

        n = sc.nextInt();
        k = sc.nextInt();

        adj = new ArrayList[n];
        deg = new int[n];
        for (int i = 0; i < n; i++)
            adj[i] = new ArrayList<>();
        for (int i = 0; i < n - 1; i++) {
            int u = sc.nextInt() - 1;
            int v = sc.nextInt() - 1;
            adj[u].add(v);
            adj[v].add(u);
            deg[u]++;
            deg[v]++;
        }
        dis = new int[n];
        Arrays.fill(dis, -1);
        Queue<Integer> q = new LinkedList<>();
        for (int i = 0; i < n; i++)
            if (deg[i] == 1) {
                dis[i] = 0;
                q.add(i);
            }
        while (!q.isEmpty()) {
            root = q.poll();
            for (int v : adj[root])
                if (dis[v] == -1) {
                    dis[v] = 0;
                    q.add(v);
                }
        }
        ok = true;
        Arrays.fill(dis, -1);
        dis[root] = 0;
        dfs(root);
        pw.println(ok ? "Yes" : "No");
        pw.flush();
        pw.close();
    }

    static int n, k;
    static int[] deg;
    static int root;
    static int[] dis;
    static boolean ok;
    static ArrayList<Integer>[] adj;


    static void dfs(int u) {
        if (deg[u] == 1) {
            if (dis[u] != k)
                ok = false;
            return;
        }
        int c = deg[u];
        if (u == root)
            c++;
        if (c < 4)
            ok = false;
        for (int v : adj[u])
            if (dis[v] == -1) {
                dis[v] = dis[u] + 1;
                dfs(v);
            }
    }

    static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

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

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

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

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}