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;
bool vis[100007];
int cnt;
vector<int> v[100007];
unordered_set<int> s[12];
int main() {
  int n, k, x, y, sz = 0;
  bool fl = 1;
  scanf("%d", &n);
  ;
  scanf("%d", &k);
  ;
  for (int i = 0; i < n - 1; ++i) {
    scanf("%d", &x);
    ;
    scanf("%d", &y);
    ;
    v[x].push_back(y);
    v[y].push_back(x);
  }
  if (n == 1) {
    cout << "No";
    return 0;
  }
  for (int i = 1; i <= n; ++i) {
    if (v[i].size() == 1) {
      vis[i] = 1;
      s[1].insert(v[i][0]);
      ++cnt;
    }
  }
  sz = 1;
  while (cnt < n && fl) {
    if (sz == k && s[sz].size() > 1) {
      fl = 0;
      break;
    }
    for (auto it : s[sz]) {
      vis[it] = 1;
      ++cnt;
      if (sz == k && v[it].size() < 3) {
        fl = 0;
        break;
      } else if (sz < k && v[it].size() < 4) {
        fl = 0;
        break;
      }
      for (int j = 0; j < v[it].size(); ++j)
        if (!vis[v[it][j]]) s[sz + 1].insert(v[it][j]);
    }
    ++sz;
  }
  if (fl && sz == k + 1)
    printf("Yes\n");
  else
    printf("NO\n");
  return 0;
}
