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;
const int maxn = 1e5 + 17;
int n, k;
vector<int> g[maxn], vec;
pair<int, int> get(int v, int p = -1, int h = 0) {
  pair<int, int> ret = {h, v};
  for (auto u : g[v])
    if (u != p) ret = max(ret, get(u, v, h + 1));
  return ret;
}
bool go(int v, int u, int p = -1) {
  vec.push_back(v);
  if (v == u) return 1;
  for (auto x : g[v])
    if (x != p && go(x, u, v)) return 1;
  vec.pop_back();
  return 0;
}
bool check(int v, int p = -1, int h = 0) {
  if (h == k) return g[v].size() == 1;
  if (p == -1 && g[v].size() < 3) return 0;
  if (p != -1 && g[v].size() < 4) return 0;
  for (auto u : g[v])
    if (u != p && !check(u, v, h + 1)) return 0;
  return 1;
}
int main() {
  ios::sync_with_stdio(0), cin.tie();
  cin >> n >> k;
  for (int i = 1; i < n; i++) {
    int v, u;
    cin >> v >> u;
    v--, u--;
    g[v].push_back(u);
    g[u].push_back(v);
  }
  {
    int t = get(0).second;
    int u = get(t).second;
    go(t, u);
  }
  if (k * 2 + 1 != vec.size()) return cout << "No\n", 0;
  int r = vec[k];
  cout << (check(vec[k]) ? "Yes" : "No") << '\n';
}
