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 long long maxn = 1e5 + 100;
long long n, k, deg[maxn], q[maxn], d[maxn], p[maxn], cnt[maxn];
vector<long long> adj[maxn];
void ex() {
  cout << "No";
  exit(0);
}
signed main() {
  cin >> n >> k;
  for (long long i = 1; i < n; i++) {
    long long u, v;
    cin >> u >> v;
    adj[u].push_back(v);
    adj[v].push_back(u);
    deg[u]++, deg[v]++;
  }
  long long ptr = 0;
  for (long long i = 1; i <= n; i++)
    if (deg[i] == 1) q[ptr++] = i, d[i] = 1;
  for (long long i = 0; i < n; i++) {
    long long u = q[i];
    if (cnt[u] < 3 and d[u] > 1) ex();
    for (auto v : adj[u]) {
      if (p[v] == u) continue;
      if (!d[v]) {
        d[v] = d[u] + 1;
        q[ptr++] = v;
      } else if (d[v] != d[u] + 1)
        ex();
      p[u] = v;
      cnt[v]++;
    }
  }
  if (d[q[n - 1]] == k + 1)
    cout << "Yes";
  else
    ex();
}
