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 <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;
}
