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 INF = 1e9 + 7;
const long long LL_INF = 1ll * INF * INF;
const int MAX_N = 100000 + 7;
template <typename T>
inline void addmod(T& a, const long long& b, const int& MOD = INF) {
  a = (a + b) % MOD;
  if (a < 0) a += MOD;
}
int n, k;
vector<int> adj[MAX_N];
bool removed[MAX_N];
int deg[MAX_N];
void solve() {
  cin >> n >> k;
  for (int i = 1; i < n; ++i) {
    int u, v;
    cin >> u >> v;
    adj[u].push_back(v);
    adj[v].push_back(u);
    deg[u]++;
    deg[v]++;
  }
  queue<int> leaves;
  for (int i = 1; i <= n; ++i)
    if (deg[i] == 1) leaves.push(i);
  for (int t = 1; t <= k; ++t) {
    if (leaves.empty()) {
      cout << "No";
      return;
    }
    bool check = true;
    vector<int> new_queue;
    while (!leaves.empty()) {
      int u = leaves.front();
      leaves.pop();
      removed[u] = true;
      for (int v : adj[u])
        if (!removed[v]) {
          deg[v]--;
          new_queue.push_back(v);
        }
    }
    sort(new_queue.begin(), new_queue.end());
    for (int i = 0; i < new_queue.size() && check;) {
      int j = i;
      while (j < new_queue.size() && new_queue[i] == new_queue[j]) ++j;
      int cnt = j - i;
      if (cnt < 3 || deg[new_queue[i]] > 1) check = false;
      leaves.push(new_queue[i]);
      i = j;
    }
    if (!check) {
      cout << "No";
      return;
    }
  }
  if (leaves.size() == 1)
    cout << "Yes";
  else
    cout << "No";
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  const bool multiple_test = false;
  int test = 1;
  if (multiple_test) cin >> test;
  for (int i = 0; i < test; ++i) {
    solve();
  }
}
