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;
int n;
map<int, set<int>> g;
bool f(int k) {
  if (k == 0) {
    if (g.size() == 1) {
      return true;
    } else {
      return false;
    }
  } else {
    map<int, int> kek;
    vector<int> fd;
    for (const auto& e : g) {
      if (e.second.size() == 0) {
        return false;
      } else if (e.second.size() == 1) {
        fd.push_back(e.first);
      }
    }
    for (auto e : fd) {
      if (g[e].size() == 0) {
        return false;
      }
      int to = *g[e].begin();
      g[to].erase(e);
      kek[to]++;
      g.erase(e);
    }
    for (auto e : kek) {
      if ((e.second < 3) || (g[e.first].size() > 1)) {
        return false;
      }
    }
    return f(k - 1);
  }
}
int main() {
  ios::sync_with_stdio(false);
  cout.tie(0);
  cin.tie(0);
  int k;
  cin >> n >> k;
  for (int i = 0; i < n - 1; ++i) {
    int v, u;
    cin >> v >> u;
    v--;
    u--;
    g[v].insert(u);
    g[u].insert(v);
  }
  if (f(k)) {
    cout << "Yes" << endl;
  } else {
    cout << "No" << endl;
  }
  return 0;
}
