#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;
}
