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 = (int)1e6 + 7;
int n, k;
int p[maxn];
vector<int> g[maxn];
pair<int, int> bfs(int st) {
  fill(p, p + n, -1);
  vector<int> d(n, 123456789);
  queue<int> q;
  q.push(st);
  d[st] = 0;
  while (!q.empty()) {
    int v = q.front();
    q.pop();
    for (int to : g[v]) {
      if (d[to] > d[v] + 1) {
        q.push(to);
        d[to] = d[v] + 1;
        p[to] = v;
      }
    }
  }
  int id = max_element(d.begin(), d.end()) - d.begin();
  return make_pair(id, d[id]);
}
bool check(int v, int p, int d = 0) {
  if (g[v].size() == 1) {
    return d == k;
  }
  bool ret = ((int)g[v].size() - (v != p)) > 2;
  for (int to : g[v]) {
    if (to == p) continue;
    ret &= check(to, v, d + 1);
  }
  return ret;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin >> n >> k;
  for (int i = 1; i < n; ++i) {
    int x, y;
    cin >> x >> y;
    --x, --y;
    g[x].push_back(y);
    g[y].push_back(x);
  }
  auto d = bfs(bfs(0).first);
  if (d.second != k * 2) {
    cout << "No" << endl;
    return 0;
  }
  int center = d.first;
  for (int i = 0; i < k; ++i) {
    center = p[center];
  }
  cout << (check(center, center) ? "Yes" : "No") << endl;
  return 0;
}
