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;
const long long MOD = 1e9 + 7;
int n, k;
set<int> edges[100000 + 10];
int deg[100000 + 10];
map<int, vector<int> > h[2];
int level = 0;
int cur = 0;
int total = 0;
int last = 0;
int main() {
  cin.tie(0);
  ios_base::sync_with_stdio(0);
  cin >> n >> k;
  for (int i = 0; i < n - 1; i++) {
    int u, v;
    cin >> u >> v;
    edges[u].insert(v);
    edges[v].insert(u);
    deg[u]++;
    deg[v]++;
  }
  if (n < 4) {
    cout << "NO" << '\n';
    return 0;
  }
  for (int i = 1; i < n + 1; i++) {
    if (deg[i] == 1) {
      h[cur][*(edges[i].begin())].push_back(i);
    }
  }
  while (1) {
    h[1 - cur].clear();
    for (auto it = h[cur].begin(); it != h[cur].end(); it++) {
      total += (*it).second.size();
      if (deg[(*it).first] > (*it).second.size() + 1) {
        cout << "NO" << '\n';
        return 0;
      } else if (deg[(*it).first] == (*it).second.size()) {
        last = 1;
        if (deg[(*it).first] < 3) {
          cout << "NO" << '\n';
          return 0;
        }
      } else {
        if (deg[(*it).first] < 4) {
          cout << "NO" << '\n';
          return 0;
        }
      }
      for (auto it1 = (*it).second.begin(); it1 != (*it).second.end(); it1++) {
        edges[(*it).first].erase((*it1));
      }
      h[1 - cur][*(edges[(*it).first].begin())].push_back((*it).first);
    }
    level++;
    cur = 1 - cur;
    if (last) {
      if (total != n - 1 || k != level) {
        cout << "NO" << '\n';
        return 0;
      }
      break;
    }
  }
  cout << "YES" << '\n';
  return 0;
}
