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.
#include <bits/stdc++.h>
using namespace std;
vector<vector<int>> adj;
pair<int, int> maxVert(int v, int p) {
  int ma = 0, maxVertex = v;
  for (int i = 0; i < adj[v].size(); i++) {
    if (adj[v][i] != p) {
      pair<int, int> res = maxVert(adj[v][i], v);
      if (res.second > ma) {
        ma = res.second;
        maxVertex = res.first;
      }
    }
  }
  return {maxVertex, ma + 1};
}
int k;
bool ultrafail = false;
int supercentre;
vector<int> maxPath;
void dfsFromMax(int start, int p, int dist) {
  maxPath.push_back(start);
  for (int i = 0; i < adj[start].size(); i++) {
    if (adj[start][i] != p) dfsFromMax(adj[start][i], start, dist - 1);
  }
  if (dist == 0) {
    if (maxPath.size() < k + 1) {
      ultrafail = true;
      return;
    }
    supercentre = maxPath[k];
    return;
  } else
    maxPath.pop_back();
}
bool isK(int v, int center, int k) {
  if (k == 0 && adj[v].size() == 1) return true;
  if (adj[v].size() < 3 || (adj[v].size() < 4 && v != supercentre))
    return false;
  for (int i = 0; i < adj[v].size(); i++) {
    if (adj[v][i] != center) {
      if (!isK(adj[v][i], v, k - 1)) return false;
    }
  }
  return true;
}
int main() {
  int n;
  cin >> n >> k;
  adj.resize(n);
  if (k > 24) {
    cout << "No" << endl;
    return 0;
  }
  for (int i = 0; i < n - 1; i++) {
    int u, v;
    cin >> u >> v;
    adj[--u].push_back(--v);
    adj[v].push_back(u);
  }
  pair<int, int> maxV = maxVert(0, -1);
  dfsFromMax(maxV.first, -1, 2 * k);
  if (ultrafail) {
    cout << "No";
    return 0;
  }
  if (isK(supercentre, -1, k))
    cout << "Yes";
  else
    cout << "No";
  return 0;
}
