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, dist[200000];
vector<long long> v[200000];
signed main() {
  cin.tie(0);
  cout.tie(0);
  ios_base::sync_with_stdio(false);
  cin >> n >> k;
  for (long long i = 1; i < n; i++) {
    long long a, b;
    cin >> a >> b;
    v[a].push_back(b);
    v[b].push_back(a);
  }
  queue<long long> q;
  for (long long i = 1; i < n + 1; i++) {
    dist[i] = 1000000000000000000;
    if (v[i].size() == 1) {
      dist[i] = 0;
      q.push(i);
    }
  }
  while (!q.empty()) {
    long long node = q.front();
    q.pop();
    for (auto x : v[node]) {
      if (dist[x] > dist[node] + 1) {
        dist[x] = dist[node] + 1;
        q.push(x);
      }
    }
  }
  long long center;
  bool found = 0;
  for (long long i = 1; i < n + 1; i++) {
    if (dist[i] == k) {
      if (found) {
        cout << "No\n";
        exit(0);
      } else {
        found = 1;
        center = i;
      }
    }
  }
  if (!found) {
    cout << "No\n";
    exit(0);
  }
  bool ok = 1;
  q.push(center);
  for (long long i = 1; i < n + 1; i++)
    ok &= ((i == center or (v[i].size() > 3 or dist[i] == 0)) and
           (i != center or v[i].size() >= 3)),
        dist[i] = 1000000000000000000;
  dist[center] = 0;
  while (!q.empty()) {
    long long node = q.front();
    q.pop();
    for (auto x : v[node]) {
      if (dist[x] > dist[node] + 1) {
        dist[x] = dist[node] + 1;
        q.push(x);
      }
    }
  }
  for (long long i = 1; i < n + 1; i++) {
    ok &= ((v[i].size() == 1 or dist[i] < k) and
           (v[i].size() > 1 or dist[i] == k));
  }
  if (ok)
    cout << "Yes\n";
  else
    cout << "No\n";
}
