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;
long long n, k;
vector<long long> dsk[100005];
long long H[100005], passed[100005], Child_cnt[100005];
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> k;
  long long u, v;
  for (long long i = 1; i <= n; i++) {
    if (i < n) {
      cin >> u >> v;
      dsk[u].push_back(v);
      dsk[v].push_back(u);
    }
    H[i] = -1;
    passed[i] = Child_cnt[i] = 0;
  }
  queue<long long> Q;
  for (long long i = 1; i <= n; i++)
    if (dsk[i].size() == 1) {
      H[i] = 0;
      Q.push(i);
    }
  while (!Q.empty()) {
    long long t = Q.front();
    Q.pop();
    if (passed[t] == 1) continue;
    passed[t] = 1;
    if (H[t] > 0 && Child_cnt[t] < 3) {
      cerr << "NO-CHILD ERROR!";
      cout << "No\n";
      return 0;
    }
    for (long long i : dsk[t])
      if (passed[i] == 0) {
        if (H[i] == -1) {
          H[i] = H[t] + 1;
          Q.push(i);
        } else if (H[i] != H[t] + 1) {
          cerr << "UNBALANCED!";
          cout << "No\n";
          return 0;
        }
        Child_cnt[i]++;
      }
  }
  long long kcnt = 0;
  for (long long i = 1; i <= n; i++) kcnt += (H[i] == k);
  if (kcnt == 1)
    cout << "Yes\n";
  else {
    cerr << "MORE THAN K HED";
    cout << "No\n";
  }
}
