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.InputStreamReader;
import java.io.PrintWriter;
import java.lang.reflect.Array;
import java.util.*;


public class Main {
    long gcd(long a, long b) {
        if (b == 0) {
            return a;
        }
        return gcd(b, a % b);
    }

    ArrayList<Integer> g[];
    int root = -1;
    int len[];

    void dfs1(int v) {
        for (int u : g[v]) {
            if (len[v] + 1 < len[u]) {
                len[u] = len[v] + 1;
                dfs1(u);
            }
        }
    }

    int lvl[];
    boolean ans = true;
    void dfsC(int v, int pr) {
        int cnt = 0;
        if(lvl[v] == k){
            for(int u : g[v]){
                if(u == pr)continue;
                cnt++;
                if(g[u].size() != 1) {
                    ans = false;
                    return;
                }
            }
        }else{
            for (int u : g[v]) {
                if (u == pr) continue;
                lvl[u] = lvl[v] + 1;
                dfsC(u, v);
                if(g[u].size() < 4) ans = false;
                cnt++;
            }
        }
        if(cnt < 3){
            ans = false;
        }
    }
    int dfsF(int v, int pr){
        int mx = len[v], mn = 0;
        for (int u : g[v]) {
            if(u == pr) continue;
            int y = dfsF(u, v);
            if(mx < y){
                mx = y;
                mn = u;
            }
        }
        if(len[v] == maxL / 2 - 1 && mx == maxL){
            root = mn;
        }
        return mx;
    }
    int k;
    int maxL = 0;

    public void solve() throws IOException {
        int n = nextInt();
        k = nextInt();
        lvl = new int[n];
        if (n < 4) {
            out.print("No");
            return;
        }
        int m = n - 1;
        g = new ArrayList[n];
        for (int i = 0; i < n; i++) {
            g[i] = new ArrayList<>();
        }
        len = new int[n];
        int cnt[] = new int[n];
        for (int w = 0; w < m; w++) {
            int a = nextInt() - 1, b = nextInt() - 1;
            g[a].add(b);
            g[b].add(a);
            cnt[a]++;
            cnt[b]++;
        }
        for (int i = 0; i < n; i++) {
            if (cnt[i] == 1) root = i;
            len[i] = Integer.MAX_VALUE;
        }
        len[root] = 0;
        dfs1(root);
        for (int i = 0; i < n; i++) {
            maxL = Math.max(maxL, len[i]);
        }
        if (maxL % 2 == 1 || maxL != 2 * k) {
            out.print("No");
            return;
        }
        dfsF(root, -1);
        Arrays.fill(lvl, Integer.MAX_VALUE);
        lvl[root] = 1;
        dfsC(root, -1);
        if(ans){
            out.print("Yes");
        }else {
            out.print("No");
        }
    }

    BufferedReader br;
    StringTokenizer sc;
    PrintWriter out;

    public static void main(String[] args) throws IOException {
        Locale.setDefault(Locale.US);
        new Main().run();
    }

    public boolean hasNext() throws IOException {
        while (sc == null || !sc.hasMoreTokens()) {
            try {
                sc = new StringTokenizer(br.readLine());
            } catch (Exception e) {
                return false;
            }
        }
        return true;
    }

    public void run() throws IOException {
        try {
            br = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
            solve();
            out.close();
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(1);
        }
    }

    public String nextToken() throws IOException {
        while (sc == null || !sc.hasMoreTokens()) {
            try {
                sc = new StringTokenizer(br.readLine());
            } catch (Exception e) {
                return null;
            }
        }
        return sc.nextToken();
    }

    public int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    public double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

    public long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }
}