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;
vector<int> g[100005];
int n, k;
int mark[100005];
int deg[100005];
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cin >> n >> k;
  for (int i = 1; i <= n - 1; ++i) {
    int u, v;
    cin >> u >> v;
    g[u].push_back(v);
    g[v].push_back(u);
  }
  if (k >= n || n <= 3) {
    cout << "No\n";
    return 0;
  }
  vector<int> q;
  int rem = n;
  for (int i = 1; i <= n; ++i)
    if (g[i].size() == 1) {
      q.push_back(i);
      mark[i] = 1;
      rem--;
    }
  int steps = 0;
  while (1) {
    if (rem == 0 && q.size() > 1) {
      cout << "No\n";
      return 0;
    }
    if (rem == 0) break;
    vector<int> nxt;
    for (int st : q) {
      for (int v : g[st]) {
        if (!mark[v]) {
          mark[v] = 1;
          nxt.push_back(v);
        }
        deg[v]++;
      }
    }
    for (int v : nxt) {
      if (deg[v] <= 2) {
        cout << "No\n";
        return 0;
      }
    }
    rem -= nxt.size();
    assert(nxt.size() > 0);
    q = nxt;
    steps++;
    if (q.size() == 1) {
      if (rem == 0) break;
      cout << "No\n";
      return 0;
    }
    for (int v : q)
      if (g[v].size() != 1 + deg[v]) {
        cout << "No\n";
        return 0;
      }
  }
  if (steps == k)
    cout << "Yes\n";
  else
    cout << "No\n";
}
