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;
const int MAXN = 1e5 + 7;
int n, k;
int colour[MAXN];
int deg[MAXN];
vector<int> graph[MAXN];
vector<int> leaves[MAXN];
int main() {
  ios_base::sync_with_stdio(false);
  cin >> n >> k;
  for (int i = 1; i < n; i++) {
    int a, b;
    cin >> a >> b;
    graph[a].push_back(b);
    graph[b].push_back(a);
    deg[a]++;
    deg[b]++;
  }
  for (int i = 1; i <= n; i++) {
    if (deg[i] == 1) {
      colour[i] = k + 1;
      leaves[0].push_back(i);
    }
  }
  int c = k + 1, i = 0;
  if (n == 1) {
    cout << "No";
    return 0;
  }
  while (c) {
    if (!leaves[i].size()) {
      cout << "No";
      return 0;
    }
    for (int v : leaves[i]) {
      int cnt = 0;
      for (int w : graph[v]) {
        if (!colour[w]) {
          cnt++;
          colour[w] = c - 1;
          leaves[i + 1].push_back(w);
        } else if ((colour[w] != c - 1) and (colour[w] != c + 1)) {
          cout << "No";
          return 0;
        } else if (colour[w] != c + 1)
          cnt++;
      }
      if ((c == 1) and (cnt or (deg[v] < 3))) {
        cout << "No";
        return 0;
      } else if (((c > 1) and (c < k + 1)) and ((cnt > 1) or (deg[v] < 4))) {
        cout << "No";
        return 0;
      }
    }
    c--;
    i++;
  }
  cout << "Yes";
  return 0;
}
