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;
template <typename IT>
ostream &print(IT b, IT e, string sep = " ", ostream &stream = cout) {
  for (IT it = b; it != e; ++it) {
    stream << *it;
    if (it + 1 != e) stream << sep;
  }
  return stream;
}
template <typename IT>
istream &read(IT b, IT e, istream &stream = cin) {
  for (IT it = b; it != e; ++it) stream >> *it;
  return stream;
}
template <typename T>
ostream &operator<<(ostream &stream, vector<T> &t) {
  return print((t).begin(), (t).end(), " ", stream);
}
template <typename T>
ostream &operator<<(ostream &stream, vector<T> &&t) {
  return print((t).begin(), (t).end(), " ", stream);
}
template <typename T>
istream &operator>>(istream &stream, vector<T> &t) {
  return read((t).begin(), (t).end(), stream);
}
template <typename T>
void print(T x, string end = "\n") {
  cout << x << end;
}
template <typename t>
void print(vector<t> arr, string sep = " ") {
  if (arr.empty()) {
    return;
  }
  print(arr.begin(), arr.end(), sep);
  cout << '\n';
}
template <typename T>
void print(vector<vector<T> > arr) {
  for (int i = 0; i < int(arr.size()); ++i) {
    cout << "[" << arr[i] << "]";
    if (i + 1 < int(arr.size())) cout << ", ";
  }
  cout << '\n';
}
template <typename T>
T _();
const long long MOD = 1e9 + 7;
template <typename T>
vector<T> operator+(const vector<T> &lhs, const vector<T> &rhs) {
  vector<T> ans(lhs);
  assert(ans.size() == rhs.size());
  for (int i = 0; i < rhs.size(); ++i) ans[i] += rhs[i];
  return ans;
}
template <typename T>
vector<T> operator+=(vector<T> &lhs, const vector<T> &rhs) {
  return lhs = lhs + rhs;
}
template <typename T>
vector<T> operator-(const vector<T> lhs, const vector<T> rhs) {
  vector<T> ans((lhs).begin(), (lhs).end());
  assert(ans.size() == rhs.size());
  for (int i = 0; i < rhs.size(); ++i) ans[i] -= rhs[i];
  return ans;
}
template <typename T>
vector<T> operator-=(vector<T> &lhs, const vector<T> &rhs) {
  return lhs = lhs - rhs;
}
template <typename T>
vector<T> append(vector<T> &lhs, const vector<T> rhs) {
  lhs.insert(lhs.end(), (rhs).begin(), (rhs).end());
  return lhs;
}
template <typename T>
T max(const vector<T> arr) {
  assert(!arr.empty());
  T ans = arr[0];
  for (auto &cur : arr) ans = max(ans, cur);
  return ans;
}
template <typename T>
T max(const set<T> s) {
  assert(!s.empty());
  return *--s.end();
}
template <typename T, typename G>
vector<T> set_max(vector<T> &base, const vector<G> &comp) {
  assert(base.size() == comp.size());
  for (int i = 0; i < (int)comp.size(); ++i) base[i] = max(base[i], comp[i]);
  return base;
}
const int N = 1e5 + 5;
vector<int> adj[N];
int deg[N];
bool is_hog(int u, int h, int p = -1) {
  vector<int> ch;
  for (int v : adj[u])
    if (v != p) ch.push_back(v);
  bool ok = true;
  if (ch.size() == 0 && h == 0) return true;
  if (ch.size() < 3) return false;
  for (int v : ch) ok &= is_hog(v, h - 1, u);
  return ok;
}
void _() {
  int n, k;
  cin >> n >> k;
  for (int i = 0; i < n - 1; ++i) {
    int u, v;
    cin >> u >> v;
    adj[u].push_back(v);
    adj[v].push_back(u);
    deg[u]++;
    deg[v]++;
  }
  vector<int> dist(n + 1, n);
  vector<int> bfs;
  vector<bool> visited(n + 1);
  for (int i = 1; i <= n; ++i)
    if (adj[i].size() <= 1) {
      dist[i] = 0;
      bfs.push_back(i);
    }
  for (int i = 0; i < bfs.size(); ++i) {
    int u = bfs[i];
    for (int v : adj[u]) {
      --deg[v];
      if (deg[v] == 1) {
        bfs.push_back(v);
        visited[v] = true;
      }
    }
  }
  int root = bfs.back();
  if (is_hog(root, k))
    print("Yes");
  else
    print("No");
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout << fixed << setprecision(15);
  _();
}
