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 main() {
  int i, j;
  int n, k;
  cin >> n >> k;
  set<int> s[n + 1];
  set<int> ss;
  for (i = 1; i < n; i++) {
    int x, y;
    cin >> x >> y;
    s[x].insert(y);
    s[y].insert(x);
  }
  for (i = 1; i <= n; i++) {
    ss.insert(i);
  }
  int loop = 0;
  while (ss.size() >= 2) {
    loop++;
    bool update = 0;
    map<int, int> m;
    vector<int> see;
    vector<int> va;
    for (auto it = ss.begin(); it != ss.end(); ++it) {
      j = *it;
      if (s[j].size() == 1) {
        va.push_back(j);
      }
    }
    for (int r = 0; r < va.size(); r++) {
      j = va[r];
      if (!s[j].size()) {
        cout << "No" << endl;
        return 0;
      }
      auto ite = s[j].begin();
      s[*ite].erase(j);
      m[*ite]++;
      see.push_back(j);
      update = 1;
    }
    for (auto mi = m.begin(); mi != m.end(); ++mi) {
      if (mi->second <= 2) {
        cout << "No" << endl;
        return 0;
      }
    }
    for (int w = 0; w < see.size(); w++) {
      ss.erase(see[w]);
    }
    if (update == 0) {
      cout << "No" << endl;
      return 0;
    }
  }
  if (k == loop)
    cout << "Yes" << endl;
  else
    cout << "No" << endl;
  return 0;
}
