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 n, k;
vector<int> adj[200013];
int parent[200013];
pair<int, int> findFarthestNode(int cur, int par) {
  parent[cur] = par;
  pair<int, int> best = make_pair(cur, 0);
  for (int next : adj[cur]) {
    if (next == par) continue;
    pair<int, int> temp = findFarthestNode(next, cur);
    temp.second++;
    if (temp.second > best.second) {
      best = temp;
    }
  }
  return best;
}
bool validate(int cur, int par, int depth) {
  if (depth > k) return false;
  if (depth < k && adj[cur].size() < 4 - (depth == 0 ? 1 : 0)) return false;
  if (depth == k && adj[cur].size() != 1) return false;
  if (depth == k && adj[cur].size() == 1) return true;
  bool answer = true;
  for (int next : adj[cur]) {
    if (next == par) continue;
    answer &= validate(next, cur, depth + 1);
  }
  return answer;
}
int main() {
  if (fopen("FILENAME.in", "r")) {
    freopen("FILENAME.in", "r", stdin);
    freopen("FILENAME.out", "w", stdout);
  }
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cin >> n >> k;
  for (int i = 0; i < n - 1; i++) {
    int a, b;
    cin >> a >> b;
    a--;
    b--;
    adj[a].push_back(b);
    adj[b].push_back(a);
  }
  pair<int, int> firstNode = findFarthestNode(0, -1);
  pair<int, int> secondNode = findFarthestNode(firstNode.first, -1);
  if (secondNode.second != 2 * k) {
    cout << "No" << endl;
    return 0;
  }
  int root = secondNode.first;
  for (int i = 0; i < k; i++) {
    root = parent[root];
  }
  if (validate(root, -1, 0)) {
    cout << "Yes" << endl;
  } else {
    cout << "No" << endl;
  }
}
