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;
vector<vector<int> > g;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int n, k;
  cin >> n >> k;
  g.resize(n);
  for (int i = 0; i < n - 1; ++i) {
    int a, b;
    cin >> a >> b;
    a--;
    b--;
    g[a].push_back(b);
    g[b].push_back(a);
  }
  queue<pair<int, int> > q;
  vector<int> vis(n);
  for (int i = 0; i < n; ++i) {
    if (g[i].size() == 1) {
      q.push({i, 0});
      vis[i] = 1;
    }
  }
  pair<int, int> curr;
  int cen = -1;
  while (q.size()) {
    curr = q.front();
    q.pop();
    if (curr.second == k) {
      if (cen >= 0) {
        cout << "No\n";
        return 0;
      }
      cen = curr.first;
    }
    for (auto v : g[curr.first]) {
      if (!vis[v]) {
        vis[v] = 1;
        q.push({v, curr.second + 1});
      }
    }
  }
  if (cen == -1) {
    cout << "No\n";
    return 0;
  }
  fill(vis.begin(), vis.end(), 0);
  q.push({cen, 0});
  vis[cen] = 1;
  while (q.size()) {
    curr = q.front();
    q.pop();
    if (curr.second == 0 and g[curr.first].size() < 3) {
      cout << "No\n";
      return 0;
    }
    if (curr.second == k and g[curr.first].size() != 1) {
      cout << "No\n";
      return 0;
    }
    if (curr.second > 0 and curr.second < k and g[curr.first].size() < 4) {
      cout << "No\n";
      return 0;
    }
    for (auto v : g[curr.first]) {
      if (!vis[v]) {
        vis[v] = 1;
        q.push({v, curr.second + 1});
      }
    }
  }
  cout << "Yes\n";
}
