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;
vector<vector<int>> graph;
vector<int> used, dist, pr;
int mdfs(int v) {
  used[v] = true;
  int res = v;
  for (int u : graph[v]) {
    if (used[u]) {
      continue;
    }
    pr[u] = v;
    dist[u] = dist[v] + 1;
    int cur = mdfs(u);
    if (dist[cur] > dist[res]) {
      res = cur;
    }
  }
  return res;
}
bool check(int v, int k) {
  used[v] = true;
  int deg = 0;
  for (int u : graph[v]) {
    if (used[u]) {
      continue;
    }
    ++deg;
    if (!check(u, k - 1)) {
      return false;
    }
  }
  if (deg == 0) {
    return k == 0;
  }
  return deg >= 3;
}
int main() {
  int n, k;
  cin >> n >> k;
  graph.resize(n);
  int from, to;
  for (int i = 0; i < n - 1; ++i) {
    cin >> from >> to;
    --from;
    --to;
    graph[from].push_back(to);
    graph[to].push_back(from);
  }
  used.resize(n);
  dist.resize(n);
  pr.resize(n);
  int l1 = mdfs(0);
  used.assign(n, 0);
  dist.assign(n, 0);
  pr.assign(n, 0);
  int l2 = mdfs(l1);
  if (dist[l2] != 2 * k) {
    cout << "No";
    return 0;
  }
  for (int i = 0; i < k; ++i) {
    l2 = pr[l2];
  }
  used.assign(n, 0);
  cout << (check(l2, k) ? "Yes" : "No");
  return 0;
}
