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;
const int N = 1100;
const int MAXN = int(1e6) + 100;
const long long mod = int(1e9) + 7;
int solution();
int main(int argc, char* const argv[]) {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  return solution();
}
int n, k;
bool u[MAXN];
vector<int> G[MAXN], newG[MAXN], graph;
int solution() {
  cin >> n >> k;
  int f, t;
  for (int i = 1; i < n; i++) {
    cin >> f >> t;
    G[f].push_back(t);
    G[t].push_back(f);
    graph.push_back(i);
  }
  graph.push_back(n);
  for (int i = 1; i <= k; i++) {
    bool deleted = false;
    for (auto c : graph) {
      newG[c].clear();
      if (G[c].size() == 1) {
        u[c] = true;
        deleted = true;
        if (G[G[c][0]].size() < 4 - (i == k)) return cout << "No\n", 0;
      }
    }
    if (!deleted) return cout << "No\n", 0;
    vector<int> newGraph;
    for (auto c : graph) {
      if (u[c]) {
        G[c].clear();
        continue;
      }
      newGraph.push_back(c);
      for (auto to : G[c]) {
        if (!u[to]) {
          newG[c].push_back(to);
        }
      }
      for (auto to : G[c]) {
        if (u[to] && newG[c].size() != 1 && i != k) return cout << "No\n", 0;
      }
      G[c] = newG[c];
    }
    graph = newGraph;
  }
  if (graph.size() != 1) return cout << "No\n", 0;
  cout << "Yes\n";
  return 0;
}
