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;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
const long long maxn = 3e5 + 1000;
const long long mod = 1e9 + 7;
const long double PI = 4 * atan((long double)1);
long long pw(long long a, long long b, long long md = mod) {
  long long res = 1;
  while (b) {
    if (b & 1) {
      res = (a * res) % mod;
    }
    a = (a * a) % mod;
    b >>= 1;
  }
  return (res);
}
int f[maxn];
bool mark[maxn];
set<int> adj[maxn], q, qq;
int n, k;
int main() {
  cin >> n >> k;
  for (int i = 0; i < n - 1; i++) {
    int u, v;
    cin >> u >> v;
    adj[v].insert(u);
    adj[u].insert(v);
  }
  for (int i = 1; i <= n; i++) {
    if (adj[i].size() == 1) {
      q.insert(i);
    }
  }
  while (n > 1) {
    for (int v : q) {
      int u = *adj[v].begin();
      qq.insert(u);
      adj[v].erase(u);
      adj[u].erase(v);
      f[u]++;
      n--;
    }
    for (int v : qq) {
      if (f[v] < 3) {
        cout << "NO";
        return (0);
        ;
      }
      f[v] = -1e9;
    }
    swap(q, qq);
    qq.clear();
    k--;
  }
  cout << ((k == 0 && n == 1) ? "Yes" : "No");
  return (0);
}
