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;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  int n, k;
  cin >> n >> k;
  if (n < 4) {
    cout << "No" << endl;
    return 0;
  }
  vector<vector<int> > g(n);
  for (int i = (0); i < (int)(n - 1); ++i) {
    int a, b;
    cin >> a >> b;
    --a, --b;
    g[a].emplace_back(b);
    g[b].emplace_back(a);
  }
  vector<int> dist(n, -1);
  queue<int> bfs;
  for (int i = (0); i < (int)(n); ++i)
    if (g[i].size() == 1) {
      bfs.push(i);
      dist[i] = 0;
    }
  while (!bfs.empty()) {
    int a = bfs.front();
    bfs.pop();
    for (int b : g[a]) {
      if (dist[b] == -1) {
        dist[b] = dist[a] + 1;
        bfs.push(b);
      }
    }
  }
  int mx = 0;
  for (int i = (0); i < (int)(n); ++i) mx = max(dist[i], mx);
  int root = -1;
  for (int i = (0); i < (int)(n); ++i)
    if (dist[i] == mx) {
      if (root != -1) {
        cout << "No" << endl;
        return 0;
      }
      root = i;
    }
  function<bool(int, int, int)> dfs = [&](int x, int p, int k) {
    if (k && g[x].size() < 4) return false;
    if (!k && g[x].size() > 1) return false;
    for (int y : g[x])
      if (y != p)
        if (dfs(y, x, k - 1) == false) return false;
    return true;
  };
  g[root].emplace_back(-1);
  if (dfs(root, -1, k))
    cout << "Yes" << endl;
  else
    cout << "No" << endl;
  return 0;
}
