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 cd, k, deg[100005], dep[100005];
set<int> edge[100005];
vector<int> block[100005], edge2[100005], ruler;
void dfs(int u, int pre) {
  block[dep[u]].push_back(u);
  for (auto v : edge2[u]) {
    if (v != pre) {
      dep[v] = dep[u] + 1;
      dfs(v, u);
    }
  }
}
int main() {
  cin >> cd >> k;
  for (int i = 1; i < cd; i++) {
    int u, v;
    cin >> u >> v;
    edge[u].insert(v);
    edge[v].insert(u);
    deg[u]++;
    edge2[u].push_back(v);
    edge2[v].push_back(u);
    deg[v]++;
  }
  for (int i = 1; i <= cd; i++) {
    if (deg[i] == 1) {
      ruler.push_back(i);
    }
  }
  int root = 0;
  for (int i = 1; i <= k; i++) {
    vector<int> tmp;
    if (ruler.size() == 0) {
      cout << "No" << '\n';
      return 0;
    }
    for (auto u : ruler) {
      for (auto v : edge[u]) {
        if (deg[v] < 3) {
          cout << "No" << '\n';
          return 0;
        }
        edge[v].erase(u);
      }
    }
    for (auto u : ruler) {
      for (auto v : edge[u]) {
        if (edge[v].size() == 1) {
          tmp.push_back(v);
        }
        if (edge[v].size() == 0) {
          root = v;
        }
      }
    }
    ruler.clear();
    while (tmp.size() != 0) {
      ruler.push_back(tmp.back());
      tmp.pop_back();
    }
  }
  dfs(root, root);
  for (int i = 1; i <= cd; i++) {
    int deg0 = 0, deg3 = 0;
    for (auto u : block[i]) {
      if (deg[u] > 3) {
        deg3++;
      } else if (deg[u] == 1) {
        deg0++;
      } else {
        cout << "No";
        return 0;
      }
    }
    if (deg[root] < 3 || (deg3 != 0 && deg0 != 0)) {
      cout << "No";
      return 0;
    }
  }
  cout << "Yes" << '\n';
}
