#include <bits/stdc++.h>
using namespace std;
template <class c>
struct rge {
  c b, e;
};
template <class c>
rge<c> range(c i, c j) {
  return rge<c>{i, j};
}
template <class c>
auto dud(c* x) -> decltype(cerr << *x, 0);
template <class c>
char dud(...);
struct debug {
  template <class c>
  debug& operator<<(const c&) {
    return *this;
  }
};
const int nax = 1e5 + 5;
vector<int> edges[nax];
int degree[nax];
bool removed[nax];
int times[nax];
void NO() {
  puts("NO");
  exit(0);
}
int main() {
  int n, k;
  scanf("%d%d", &n, &k);
  for (int i = 0; i < n - 1; ++i) {
    int a, b;
    scanf("%d%d", &a, &b);
    edges[a].push_back(b);
    edges[b].push_back(a);
    degree[a]++;
    degree[b]++;
  }
  vector<int> q;
  for (int i = 1; i <= n; ++i) {
    if (degree[i] == 1) {
      q.push_back(i);
    }
  }
  for (int rep = 0; rep < k; ++rep) {
    for (int x : q) {
      removed[x] = true;
    }
    if (q.empty()) {
      NO();
    }
    set<int> must, can;
    for (int x : q) {
      for (int y : edges[x]) {
        if (!removed[y]) {
          ++times[y];
          must.insert(y);
          if (--degree[y] == (rep == k - 1 ? 0 : 1)) {
            can.insert(y);
          }
        }
      }
    }
    if (must != can) {
      NO();
    }
    for (int x : must) {
      if (times[x] < 3) {
        NO();
      }
    }
    q.clear();
    for (int x : must) {
      q.push_back(x);
    }
  }
  vector<int> tmp;
  for (int i = 1; i <= n; ++i) {
    if (!removed[i]) {
      tmp.push_back(i);
    }
  }
  if ((int)tmp.size() != 1) {
    NO();
  }
  puts("YES");
}
