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 dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
const long long linf = 4000000000000000000LL;
const long long inf = 998244353;
const long double pi = 3.1415926535;
void pv(vector<int> a) {
  for (auto& x : a) cout << x << " ";
  cout << '\n';
}
void pv(vector<long long> a) {
  for (auto& x : a) cout << x << " ";
  cout << '\n';
}
void pv(vector<vector<int> > a) {
  for (int i = (0); i < (int(a.size())); ++i) {
    cout << i << '\n';
    pv(a[i]);
    cout << '\n';
  }
}
void pv(vector<vector<long long> > a) {
  for (int i = (0); i < (int(a.size())); ++i) {
    cout << i << '\n';
    pv(a[i]);
  }
  cout << '\n';
}
void pv(vector<string> a) {
  for (auto& x : a) cout << x << '\n';
  cout << '\n';
}
void setIO(string second) {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  if (int(second.size())) {
    freopen((second + ".in").c_str(), "r", stdin);
    if (second != "test2") freopen((second + ".out").c_str(), "w", stdout);
  }
}
int n, k;
vector<vector<int> > adj;
vector<int> depth;
bool dfs(int i, int p) {
  int size = int(adj[i].size());
  size -= (p != -1);
  if (size < 3 && !(size == 0 && depth[i] == k)) return 0;
  for (auto& x : adj[i]) {
    if (x == p) continue;
    depth[x] = depth[i] + 1;
    if (!dfs(x, i)) return 0;
  }
  return 1;
}
int main() {
  setIO("");
  cin >> n >> k;
  adj.resize(n);
  for (int i = (0); i < (n - 1); ++i) {
    int x, y;
    cin >> x >> y;
    adj[--x].push_back(--y);
    adj[y].push_back(x);
  }
  if (n == 1) {
    cout << "NO" << '\n';
    return 0;
  }
  deque<int> todo;
  for (int i = (0); i < (n); ++i) {
    if (int(adj[i].size()) == 1) todo.push_back(i);
  }
  vector<int> size(n);
  for (int i = (0); i < (n); ++i) size[i] = int(adj[i].size());
  int center = -1;
  while (int(todo.size())) {
    int i = todo.front();
    todo.pop_front();
    center = i;
    for (auto& x : adj[i]) {
      size[x]--;
      if (size[x] == 1) todo.push_back(x);
    }
  }
  depth.resize(n);
  depth[center] = 0;
  if (!dfs(center, -1))
    cout << "NO" << '\n';
  else {
    cout << (*max_element(depth.begin(), depth.end()) == k ? "YES" : "NO")
         << '\n';
  }
}
