#include <bits/stdc++.h>
using namespace std;
template <class T>
ostream &operator<<(ostream &os, const pair<T, T> &p) {
  return os << "(" << p.first << "," << p.second << ")";
}
template <class T>
ostream &operator<<(ostream &os, const pair<const T, T> &p) {
  return os << "(" << p.first << "," << p.second << ")";
}
template <class T>
ostream &operator<<(ostream &os, const array<T, 3> &p) {
  return os << "(" << p[0] << "," << p[1] << "," << p[2] << ")";
}
template <class T>
ostream &operator<<(ostream &os, const vector<T> &p) {
  for (auto x : p) os << x << ' ';
  return os;
}
const double EPS = 1e-9, PI = acos(-1);
const long long LINF = 0x3f3f3f3f3f3f3f3f, mod = 1e9;
const long long INF = 0x3f3f3f3f, SZ = 1e5 + 10;
vector<long long> g[SZ];
set<long long> cor[SZ];
bool vis[SZ];
set<long long> kk[SZ];
int32_t main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  long long n, k;
  cin >> n >> k;
  for (long long i = 1; i < n; i++) {
    long long u, v;
    cin >> u >> v;
    g[u].push_back(v);
    g[v].push_back(u);
  }
  if (n <= 3) return cout << "No" << '\n', 0;
  for (long long i = 1; i < n + 1; i++)
    if (g[i].size() == 1) {
      kk[0].insert(i);
      cor[i].insert(0);
    }
  long long res = 0;
  while (kk[res].size() != 0) {
    for (auto v : kk[res]) {
      vis[v] = 1;
      for (auto u : g[v])
        if (vis[u] == 0) {
          kk[res + 1].insert(u);
          cor[u].insert(res + 1);
          if (cor[u].size() > 1) return cout << "No" << '\n', 0;
        }
    }
    res++;
  }
  res--;
  if (res != k) return cout << "No" << '\n', 0;
  if (kk[res].size() != 1) return cout << "No" << '\n', 0;
  for (auto x : kk[res])
    if (g[x].size() < 3) return cout << "No" << '\n', 0;
  for (auto x : kk[0])
    if (g[x].size() != 1) return cout << "No" << '\n', 0;
  for (long long i = 1; i < res; i++) {
    for (auto x : kk[i])
      if (g[x].size() < 4) return cout << "No" << '\n', 0;
  }
  cout << "Yes" << '\n';
  return 0;
}
