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<vector<int> > g;
vector<int> u, d, p;
void df(int v) {
  u[v] = 1;
  for (int i = 0; i < g[v].size(); ++i) {
    int to = g[v][i];
    if (!u[to]) {
      d[to] = d[v] + 1;
      p[to] = v;
      df(to);
    }
  }
}
bool dfs(int v) {
  u[v] = 1;
  if (d[v] > k) return false;
  if (d[v] == 0 && g[v].size() < 3) return false;
  if (d[v] != 0 && d[v] < k && g[v].size() < 4) return false;
  if (d[v] == k && g[v].size() != 1) return false;
  for (int i = 0; i < g[v].size(); ++i) {
    int to = g[v][i];
    if (!u[to]) {
      if (!dfs(to)) return false;
    }
  }
  return true;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin >> n >> k;
  g.resize(n);
  for (int i = 0; i < n - 1; ++i) {
    int a, b;
    cin >> a >> b;
    --a;
    --b;
    g[a].push_back(b);
    g[b].push_back(a);
  }
  if (n == 1) {
    cout << "No";
    return 0;
  }
  int s = 0;
  while (g[s].size() != 1) ++s;
  p.assign(n, s);
  d.assign(n, 0);
  u.assign(n, 0);
  df(s);
  s = 0;
  while (s < n && d[s] != k + k) ++s;
  if (s == n) {
    cout << "No";
    return 0;
  }
  for (int i = 0; i < k; ++i) s = p[s];
  p.assign(n, s);
  d.assign(n, 0);
  u.assign(n, 0);
  df(s);
  u.assign(n, 0);
  cout << (dfs(s) ? "Yes" : "No");
  return 0;
}
