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.util.*;
import java.io.*;
import java.lang.*;
import java.math.*;
public class B {
    public static int n;
    public static int k;
    public static boolean[] visited;
    public static int[] rank;
    public static int[] parent;
    public static ArrayList<ArrayList<Integer>> adj;
    public static ArrayList<ArrayList<Integer>> child;
    public static void main(String[] args) throws Exception {
        BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
        // Scanner scan = new Scanner(System.in);
        PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
        // int n = Integer.parseInt(bf.readLine());
        StringTokenizer st = new StringTokenizer(bf.readLine());
        // int[] a = new int[n]; for(int i=0; i<n; i++) a[i] = Integer.parseInt(st.nextToken());
        n = Integer.parseInt(st.nextToken());
        k = Integer.parseInt(st.nextToken());
        adj = new ArrayList<ArrayList<Integer>>();
        child = new ArrayList<ArrayList<Integer>>();
        for(int i=0; i<n; i++) adj.add(new ArrayList<Integer>());
        for(int i=0; i<n; i++) child.add(new ArrayList<Integer>());
        for(int i=0; i<n-1; i++) {
          st = new StringTokenizer(bf.readLine());
          int v1 =  Integer.parseInt(st.nextToken())-1;
          int v2 =  Integer.parseInt(st.nextToken())-1;
          adj.get(v1).add(v2);
          adj.get(v2).add(v1);
        }

        visited = new boolean[n];
        rank = new int[n];
        parent = new int[n];
        parent[0] = -1;
        dfs_farthest(0, 0);
        int max = -1; int max_index = -1;
        for(int i=0; i<n; i++) {
          if(rank[i] > max) {
            max = rank[i];
            max_index = i;
          }
        }
        visited = new boolean[n];
        rank = new int[n];
        parent[max_index] = -1;
        dfs_farthest(max_index, 0);
        int max_2 = -1; int max_index_2 = -1;
        for(int i=0; i<n; i++) {
          if(rank[i] > max_2) {
            max_2 = rank[i];
            max_index_2 = i;
          }
        }
        if(max_2 % 2 != 0) {
          out.println("No");
          out.close();
          System.exit(0);
        }
        for(int i=0; i<max_2/2; i++) {
          max_index_2 = parent[max_index_2];
        }
        int center = max_index_2;
        int depth = max_2/2;
        visited = new boolean[n];
        rank = new int[n];
        parent[center] = -1;
      //  out.println((center+1));
        dfs(center, 0);
        //for(int i : child.get(2)) out.println(i);
        for(int i=0; i<n; i++) {
          if(child.get(i).size() == 0) {
            if(rank[i] != depth) {
              out.println("No");
              out.close();
              System.exit(0);
            }
          }
          else if(child.get(i).size() < 3) {
            out.println("No");
            out.close();
            System.exit(0);
          }
        }
        if(depth != k) {
          out.println("No");
          out.close();
          System.exit(0);
        }
        out.println("Yes");



        // int n = scan.nextInt();

        out.close(); System.exit(0);
    }
    public static void dfs(int v, int r) {
      visited[v] = true;
      rank[v] = r;
      for(int i : adj.get(v)) {
        if(!visited[i]) {
          child.get(v).add(i);
          parent[i] = v;
          dfs(i, r+1);
        }
      }
    }
    public static void dfs_farthest(int v, int r) {
      visited[v] = true;
      rank[v] = r;
      for(int i : adj.get(v)) {
        if(!visited[i]) {
          parent[i] = v;
          dfs_farthest(i, r+1);
        }
      }
    }
}
