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 is_khog(vector<int> vertices, vector<vector<int>> edges, int K);
int main() {
  int N, K;
  cin >> N >> K;
  int ms = 4;
  for (int i = 2; i <= K; ++i) {
    ms *= 3;
    if (ms > N) {
      cout << "No" << endl;
      return 0;
    }
  }
  vector<int> vertices;
  for (int i = 1; i <= N; ++i) {
    vertices.push_back(i);
  }
  vector<vector<int>> E(N + 1);
  for (int i = 1; i < N; ++i) {
    int u, v;
    cin >> u >> v;
    E[u].push_back(v);
    E[v].push_back(u);
  }
  if (is_khog(vertices, E, K)) {
    cout << "Yes" << endl;
  } else {
    cout << "No" << endl;
  }
}
bool is_khog(vector<int> vertices, vector<vector<int>> edges, int K) {
  map<int, int> deg;
  vector<int> rem;
  for (auto &v : vertices) {
    if (edges[v].size() == 1) {
      int u = edges[v][0];
      deg[u]++;
    } else {
      rem.push_back(v);
    }
  }
  for (auto &v : deg) {
    if (v.second < 3) {
      return false;
    }
  }
  if (K == 1) {
    return (deg.size() == 1);
  }
  for (auto &v : deg) {
    vector<int> &adj = edges[v.first];
    bool f = false;
    while (adj.size() > 1) {
      int u = adj.back();
      if (edges[u].size() > 1) {
        if (f) {
          return false;
        }
        f = true;
        swap(adj[adj.size() - 1], adj[0]);
      } else {
        adj.pop_back();
      }
    }
  }
  return is_khog(rem, edges, K - 1);
}
