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>
#pragma GCC optimize("Ofast")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#pragma GCC optimize("-ffloat-store")
using namespace std;
const auto start_time = std::chrono::high_resolution_clock::now();
void aryanc403() {}
const long long int INF = 0xFFFFFFFFFFFFFFFL;
long long int seed;
mt19937 rng(seed = chrono::steady_clock::now().time_since_epoch().count());
inline long long int rnd(long long int l = 0, long long int r = INF) {
  return uniform_int_distribution<long long int>(l, r)(rng);
}
class CMP {
 public:
  bool operator()(pair<long long int, long long int> a,
                  pair<long long int, long long int> b) {
    return !(a.first < b.first || (a.first == b.first && a.second <= b.second));
  }
};
void add(map<long long int, long long int> &m, long long int x,
         long long int cnt = 1) {
  auto jt = m.find(x);
  if (jt == m.end())
    m.insert({x, cnt});
  else
    jt->second += cnt;
}
void del(map<long long int, long long int> &m, long long int x,
         long long int cnt = 1) {
  auto jt = m.find(x);
  if (jt->second <= cnt)
    m.erase(jt);
  else
    jt->second -= cnt;
}
bool cmp(const pair<long long int, long long int> &a,
         const pair<long long int, long long int> &b) {
  return a.first < b.first || (a.first == b.first && a.second < b.second);
}
const long long int mod = 1000000007L;
long long int T, n, i, j, k, in, cnt, l, r, u, v, x, y;
long long int m;
string s;
vector<vector<long long int> > e;
vector<long long int> a;
int main(void) {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  {
    cin >> n >> k;
    bool fl = true;
    if (n <= 3) fl = false;
    e.resize(n);
    for (i = 0; i < (n - 1); ++i) {
      cin >> u >> v;
      u--;
      v--;
      e[u].push_back(v);
      e[v].push_back(u);
    }
    long long int rt = -1;
    for (i = 0; i < (n); ++i) {
      if (((long long int)(e[i]).size()) == 1)
        a.push_back(i);
      else if (((long long int)(e[i]).size()) < 4) {
        if (rt != -1 || ((long long int)(e[i]).size()) != 3)
          fl = false;
        else
          rt = i;
      }
    }
    vector<bool> vis(n);
    while (k--) {
      if (!fl || a.empty()) {
        fl = false;
        break;
      };
      for (auto x : a) vis[x] = true;
      vector<long long int> b;
      for (auto x : a) {
        bool gl = false;
        for (auto y : e[x]) {
          if (vis[y]) continue;
          if (gl) {
            fl = false;
            break;
          }
          gl = true;
          b.push_back(y);
        }
        if (!gl) {
          fl = false;
        }
      };
      a.swap(b);
      sort(begin(a), end(a));
      a.erase(unique(begin(a), end(a)), a.end());
    };
    if (a.empty())
      fl = false;
    else {
      vis[a[0]] = true;
      if (rt != -1 && a[0] != rt) fl = false;
    };
    for (auto x : vis)
      if (!x) fl = false;
    cout << (fl ? "YES" : "NO") << "\n";
  }
  aryanc403();
  return 0;
}
