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;
long long int n, k, l;
vector<vector<long long int> > adj;
vector<bool> visited;
long long int d[100006] = {INT_MAX};
long long int MOD = 1000000007;
long long int level[100006];
long long int dis2[100006];
long long int degree[100006] = {0};
long long int distance(long long int x) {
  long long int last = x;
  for (long long int j = 1; j <= n; j++) d[j] = INT_MAX;
  queue<long long int> q;
  q.push(x);
  d[x] = 0;
  long long int node = x;
  while (!q.empty()) {
    node = q.front();
    q.pop();
    for (auto it : adj[node]) {
      if (d[it] > (d[node] + 1)) {
        d[it] = d[node] + 1;
        q.push(it);
      }
    }
  }
  return node;
}
void get_farthest2(int node) {
  int i;
  for (i = 0; i <= 100001; i++) {
    dis2[i] = MOD;
  }
  dis2[node] = 0;
  queue<int> q;
  q.push(node);
  while (!q.empty()) {
    int x = q.front();
    q.pop();
    for (auto it : adj[x]) {
      if (dis2[it] > (dis2[x] + 1)) {
        dis2[it] = dis2[x] + 1;
        q.push(it);
      }
    }
  }
}
int main() {
  for (long long int i = 0; i <= 100001; i++) {
    level[i] = MOD;
    degree[i] = 0;
  }
  long long int i, a, b;
  cin >> n >> k;
  if (n == 1) {
    cout << "No" << endl;
    return 0;
  }
  adj.resize(n + 1);
  long long int center = 0;
  for (i = 1; i < n; i++) {
    cin >> a >> b;
    adj[a].push_back(b);
    adj[b].push_back(a);
    degree[a]++;
    degree[b]++;
  }
  long long int x = distance(1);
  long long int y = distance(x);
  get_farthest2(y);
  long long int ans = 1;
  if ((d[y] % 2 == 1) || k > n || (dis2[x] % 2 == 1)) {
    cout << "No" << endl;
    return 0;
  }
  for (i = 1; i <= n; i++)
    if ((d[i] == dis2[i]) && (adj[i].size() >= 3) && (d[i] == (d[y] / 2))) {
      center = i;
      break;
    }
  if (center == 0) {
    cout << "No" << endl;
    return 0;
  }
  queue<int> qu;
  long long int centre = center;
  qu.push(centre);
  level[centre] = 1;
  while (!qu.empty()) {
    int xx = qu.front();
    qu.pop();
    if (xx == centre && degree[xx] < 3) {
      cout << "No";
      return 0;
    } else if ((degree[xx] < 4) && (level[xx] <= k) && (xx != centre)) {
      cout << "No";
      return 0;
    } else if (level[xx] > k && degree[xx] != 1) {
      cout << "No";
      return 0;
    }
    for (auto it : adj[xx]) {
      if (level[it] > level[xx] + 1) {
        level[it] = level[xx] + 1;
        qu.push(it);
      }
    }
  }
  cout << "Yes" << endl;
  return 0;
}
