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 = 1e5 + 10;
vector<int> g[N];
int deg[N];
bool check(int u, int p, int k);
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int n, k;
  cin >> n >> k;
  for (int i = 1; i <= n - 1; ++i) {
    int u, v;
    cin >> u >> v;
    g[u].push_back(v);
    g[v].push_back(u);
    ++deg[u];
    ++deg[v];
  }
  vector<int> cur, nxt;
  for (int i = 1; i <= n; ++i) {
    if (deg[i] == 1) {
      cur.push_back(i);
    }
  }
  while (!cur.empty()) {
    nxt.clear();
    for (auto &u : cur) {
      for (auto &v : g[u]) {
        --deg[v];
        if (deg[v] == 1) {
          nxt.push_back(v);
        }
      }
    }
    swap(cur, nxt);
  }
  int root = (nxt.empty() ? 1 : nxt[0]);
  if (check(root, 0, k)) {
    cout << "Yes\n";
  } else {
    cout << "No\n";
  }
}
bool check(int u, int p, int k) {
  int ch = (g[u].size() - (p != 0));
  if (k == 0) {
    return ch == 0;
  } else if (ch < 3) {
    return false;
  } else {
    for (auto &v : g[u]) {
      if (v != p and !check(v, u, k - 1)) {
        return false;
      }
    }
    return true;
  }
}
