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;
#pragma GCC optimize("O3")
long long gcd(long long x, long long y) { return y ? gcd(y, x % y) : x; }
const int MAXN = 3e5 + 10;
void solve(int t) {}
int n, k;
set<int> graph[MAXN];
int main(int argc, char* argv[]) {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  cin >> n >> k;
  if (n == 1) {
    cout << "NO" << '\n';
    return 0;
  }
  queue<int> q;
  for (auto i = (0); i < (n - 1); i++) {
    int u, v;
    cin >> u >> v;
    graph[u].insert(v);
    graph[v].insert(u);
  }
  for (auto i = (1); i < (n + 1); i++)
    if (graph[i].size() == 1) q.push(i);
  int ok = 1;
  for (auto i = (0); i < (k); i++) {
    map<int, int> cnt;
    int len = q.size();
    while (len--) {
      auto f = q.front();
      q.pop();
      for (auto j : graph[f]) {
        cnt[j]++;
        graph[j].erase(f);
      }
      graph[f].clear();
    };
    ;
    for (auto p : cnt) {
      if (p.second < 3) ok = 0;
      if (i == k - 1 && graph[p.first].size() != 0) ok = 0;
      if (i < k - 1 && graph[p.first].size() != 1) ok = 0;
    }
    for (auto p : cnt)
      if (graph[p.first].size() == 1) q.push(p.first);
    if (!ok) break;
  }
  if (q.size() != 0) ok = 0;
  cout << (ok ? "YES" : "NO") << '\n';
  return 0;
}
