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;
using ll = long long;
const int MOD = 998244353;
const int MAXN = (int)1e5 + 5;
int n, k;
vector<int> e[MAXN];
int deg[MAXN], used[MAXN];
int main() {
  cin >> n >> k;
  int a, b;
  for (int i = 0; i < n - 1; ++i) {
    scanf("%d%d", &a, &b);
    e[a].push_back(b);
    e[b].push_back(a);
    deg[a]++;
    deg[b]++;
  }
  vector<int> q;
  for (int i = 1; i <= n; ++i)
    if (deg[i] == 2) {
      cout << "No";
      return 0;
    } else if (deg[i] == 1)
      q.push_back(i);
  int rem = n;
  while (rem > 4 && k > 1) {
    set<int> touched;
    for (int x : q) {
      for (int v : e[x])
        if (!used[v]) {
          if (!touched.count(v) && deg[v] < 4) {
            cout << "No";
            return 0;
          }
          touched.insert(v);
          deg[v]--;
        }
      used[x] = 1;
      rem--;
    }
    q.clear();
    for (int x : touched)
      if (deg[x] > 1) {
        cout << "No";
        return 0;
      } else
        q.push_back(x);
    k--;
  }
  if (k == 1 && rem >= 4) {
    set<int> touched;
    for (int x : q)
      for (int v : e[x])
        if (!used[v]) touched.insert(v);
    if (touched.size() == 1)
      cout << "Yes";
    else
      cout << "No";
  } else
    cout << "No";
  return 0;
}
