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, d[100001], u[100001];
vector<int> gr[100001];
int check(int i, int p) {
  if (gr[i].size() == 1) {
    d[i] = 1;
    return 1;
  }
  if (gr[i][0] == p) swap(gr[i][0], gr[i][1]);
  for (auto x : gr[i]) {
    if (x != p) {
      if (check(x, i)) {
        if (d[x] != d[gr[i][0]]) return 0;
      } else
        return 0;
    }
  }
  d[i] = d[gr[i][0]] + 1;
  return 1;
}
int main() {
  cin >> n >> k;
  if (n < 4) {
    cout << "No";
    return 0;
  }
  queue<int> q;
  for (int i = 1; i < n; i++) {
    int a, b;
    cin >> a >> b;
    gr[a].push_back(b);
    gr[b].push_back(a);
  }
  for (int i = 1; i <= n; i++) {
    if (gr[i].size() == 1) {
      q.push(i);
      d[i] = 1;
    } else if (gr[i].size() == 3) {
      for (int j = i + 1; j <= n; j++) {
        if (gr[j].size() != 1 && gr[j].size() < 4) {
          cout << "No";
          return 0;
        }
      }
      if (check(i, 0) && d[i] == k + 1)
        cout << "Yes";
      else
        cout << "No";
      return 0;
    } else if (gr[i].size() < 3) {
      cout << "No";
      return 0;
    }
  }
  while (!q.empty()) {
    int t = q.front(), duck = 0;
    q.pop();
    u[t] = 1;
    for (auto x : gr[t]) {
      if (d[x] == 0) {
        d[x] = d[t] + 1;
        q.push(x);
      } else if (d[x] != d[t] - 1 && u[x]) {
        cout << "No";
        return 0;
      }
    }
    if (q.empty()) {
      if (d[t] == k + 1)
        cout << "Yes";
      else
        cout << "No";
      return 0;
    }
  }
  cout << "Yes";
}
