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;
int lv[100005];
vector<int> G[100005];
bool solve() {
  if (N < 4) return false;
  queue<int> q;
  for (int i = 1; i <= N; i++)
    if (G[i].size() == 1) {
      lv[i] = 1;
      q.push(i);
    }
  int Maxlv = 1;
  while (!q.empty()) {
    int u = q.front();
    Maxlv = max(Maxlv, lv[u]);
    q.pop();
    int deg = G[u].size();
    int vpc = 0, vnc = 0;
    for (int v : G[u]) {
      if (lv[u] == lv[v]) return false;
      if (lv[u] != 1 && lv[v] == lv[u] - 1) vpc++;
      if (lv[v] == lv[u] + 1) vnc++;
      if (lv[v] == 0) {
        lv[v] = lv[u] + 1;
        q.push(v);
        vnc++;
      }
    }
    if (lv[u] != 1) {
      if (lv[u] != K + 1) {
        if (vpc < 3 || vnc != 1 || vpc != deg - 1) return false;
      } else {
        if (vpc < 3 || vpc != deg) return false;
      }
    }
  }
  return Maxlv == K + 1;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cin >> N >> K;
  int a, b;
  for (int i = 1; i <= N - 1; i++) {
    cin >> a >> b;
    G[a].push_back(b);
    G[b].push_back(a);
  }
  bool ok = solve();
  cout << ((ok) ? "Yes" : "No") << '\n';
  return 0;
}
