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;
bool is_hedgehog(int node, int parent, int k, vector<vector<int>> &edges) {
  if (k > 0) {
    if (edges[node].size() < 4) return false;
    for (int n : edges[node]) {
      if (n == parent) continue;
      if (!is_hedgehog(n, node, k - 1, edges)) return false;
    }
    return true;
  } else {
    if (edges[node].size() != 1) return false;
    return true;
  }
}
int main() {
  int n, k;
  cin >> n >> k;
  vector<vector<int>> edges(n + 1);
  for (int i = 0; i < n - 1; i++) {
    int a, b;
    cin >> a >> b;
    edges[a].push_back(b);
    edges[b].push_back(a);
  }
  deque<int> q = {1};
  vector<int> parent(n + 1);
  vector<int> distance(n + 1);
  parent[1] = 1;
  int last_popped;
  while (!q.empty()) {
    int x = q.front();
    last_popped = x;
    q.pop_front();
    for (int n : edges[x]) {
      if (n == parent[x]) continue;
      parent[n] = x;
      q.push_back(n);
    }
  }
  q = {last_popped};
  parent[last_popped] = last_popped;
  distance[last_popped] = 0;
  while (!q.empty()) {
    int x = q.front();
    last_popped = x;
    q.pop_front();
    for (int n : edges[x]) {
      if (n == parent[x]) continue;
      distance[n] = distance[x] + 1;
      parent[n] = x;
      q.push_back(n);
    }
  }
  int diameter = distance[last_popped];
  if (diameter % 2) {
    cout << "No" << endl;
    return 0;
  }
  int radius = diameter / 2;
  int center = last_popped;
  while (radius--) {
    center = parent[center];
  }
  if (edges[center].size() < 3) {
    cout << "No" << endl;
    return 0;
  }
  bool ok = true;
  for (int n : edges[center]) {
    if (!is_hedgehog(n, center, k - 1, edges)) {
      ok = false;
      break;
    }
  }
  if (!ok) {
    cout << "No" << endl;
    return 0;
  }
  cout << "Yes" << endl;
  return 0;
}
