#include <bits/stdc++.h>
using namespace std;
vector<int> v[100005];
int vis[100005], dd[100005];
int main() {
  ios_base::sync_with_stdio(false);
  int n, k;
  cin >> n >> k;
  for (int i = 1; i <= n - 1; i++) {
    int x, y;
    cin >> x >> y;
    v[x].push_back(y);
    v[y].push_back(x);
  }
  if (n <= 3) {
    cout << "No";
    return 0;
  }
  vector<int> v1;
  for (int i = 1; i <= n; i++)
    if (v[i].size() == 1) v1.push_back(i), vis[i] = 1;
  for (int ii = 1; ii <= k; ii++) {
    set<int> prob;
    for (__typeof(v1.begin()) it = v1.begin(); it != v1.end(); it++) {
      int at = *it;
      for (__typeof(v[at].begin()) it1 = v[at].begin(); it1 != v[at].end();
           it1++) {
        int to = *it1;
        if (vis[to] == 0) prob.insert(to), dd[to]++;
      }
    }
    if (ii == k) {
      if (prob.size() != 1) {
        cout << "No";
        return 0;
      }
      int x = *prob.begin();
      if (dd[x] != v[x].size()) {
        cout << "No";
        return 0;
      }
      if (dd[x] < 3) {
        cout << "No";
        return 0;
      }
    } else {
      v1.clear();
      for (__typeof(prob.begin()) it = prob.begin(); it != prob.end(); it++) {
        vis[*it] = 1;
        v1.push_back(*it);
        if (dd[*it] < 3) {
          cout << "No";
          return 0;
        }
        if (dd[*it] != int(v[*it].size()) - 1) {
          cout << "No";
          return 0;
        }
      }
    }
  }
  cout << "Yes";
  return 0;
}
