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(0);
  int n, k;
  cin >> n >> k;
  vector<vector<int> > g(n);
  for (int step = 1; step < n; step++) {
    int u, v;
    cin >> u >> v;
    g[u - 1].push_back(v - 1);
    g[v - 1].push_back(u - 1);
  }
  auto Check = [&]() {
    vector<int> dep(n, -1);
    vector<bool> vis(n, false);
    queue<int> q;
    for (int i = 0; i < n; i++) {
      if (g[i].size() > 1) continue;
      q.push(i);
      dep[i] = 0;
    }
    while (!q.empty()) {
      int u = q.front();
      q.pop();
      vis[u] = true;
      bool foundFather = false;
      for (auto v : g[u]) {
        if (vis[v]) continue;
        if (foundFather) return false;
        foundFather = true;
        if (dep[v] > -1) {
          if (dep[v] != dep[u] + 1) return false;
        } else {
          q.push(v);
          dep[v] = dep[u] + 1;
        }
      }
      if (foundFather) {
        if (g[u].size() > 1 && g[u].size() < 4) return false;
      } else {
        if (g[u].size() < 3 || dep[u] != k) return false;
      }
    }
    return true;
  };
  cout << (Check() ? "Yes" : "No") << endl;
  return 0;
}
