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;
struct Node {
  int init_deg;
  int c_deg;
  int level = 0;
  bool removed = false;
  vector<int> edges;
  void add(int edge) {
    init_deg++;
    c_deg++;
    edges.push_back(edge);
  }
};
int n, k;
vector<Node> graph;
queue<int> hq;
bool unhedge(int node) {
  if (graph[node].removed) {
    return true;
  }
  int parent = graph[node].edges[0];
  graph[parent].level = graph[node].level + 1;
  int pp_edge = -1;
  int child_ct = 0;
  for (int edge : graph[parent].edges) {
    if (graph[edge].c_deg == 1) {
      if (graph[edge].level + 1 != graph[parent].level) {
        return false;
      }
      child_ct++;
      graph[edge].removed = true;
    } else {
      if (pp_edge == -1) {
        pp_edge = edge;
      } else {
        return false;
      }
    }
  }
  if (child_ct < 3) {
    return false;
  }
  if (pp_edge == -1) {
    return graph[parent].level == k;
  }
  graph[parent].edges.clear();
  graph[parent].edges.push_back(pp_edge);
  graph[parent].c_deg = 1;
  hq.push(parent);
  return true;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cin >> n >> k;
  graph = vector<Node>(n);
  for (int i = 0; i < n - 1; i++) {
    int u, v;
    cin >> u >> v;
    u--;
    v--;
    graph[u].add(v);
    graph[v].add(u);
  }
  if (n == 1) {
    cout << "No" << endl;
    return 0;
  }
  for (int i = 0; i < n; i++) {
    if (graph[i].init_deg == 1) {
      hq.push(i);
    }
  }
  while (hq.size() > 0) {
    if (!unhedge(hq.front())) {
      cout << "No" << endl;
      return 0;
    }
    hq.pop();
  }
  cout << "Yes" << endl;
  return 0;
}
