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>
#pragma GCC optimize("Ofast")
using namespace std;
queue<int> q;
vector<int> child[100001];
int lay[100001], cnt[100001];
int main() {
  ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  int n, k, a, b, flag, cc = 0;
  cin >> n >> k;
  for (int i = 1; i < n; ++i)
    cin >> a >> b, child[a].push_back(b), child[b].push_back(a);
  for (int i = 1; i <= n; ++i)
    if (child[i].size() == 1) q.push(i), lay[i] = 1, cnt[i] = 3;
  while (!q.empty()) {
    a = q.front(), q.pop();
    if (cnt[a] < 3) return cout << "No\n", 0;
    flag = 0;
    for (int i : child[a])
      if (!lay[i]) {
        ++cnt[i], lay[i] = lay[a] + 1, q.push(i), flag = 1;
      } else {
        if (lay[i] != lay[a] + 1 && lay[i] != lay[a] - 1)
          return cout << "No\n", 0;
        if (lay[i] == lay[a] + 1) ++cnt[i], flag = 1;
      }
    if (lay[a] == k + 1) flag = 1;
    if (!flag) return cout << "No\n", 0;
  }
  for (int i = 1; i <= n; ++i)
    if (!lay[i]) return cout << "No\n", 0;
  for (int i = 1; i <= n; ++i)
    if (lay[i] == k + 1) ++cc;
  if (*max_element(lay + 1, lay + n + 1) != k + 1 || cc != 1)
    cout << "No\n";
  else
    cout << "Yes\n";
}
