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 n, m, k, x, y;
string abc = "abcdefghijklmnopqrstuvwxyz";
string ABC = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
vector<long long> v[100005];
vector<long long> w;
set<long long> s;
vector<pair<long long, long long> > pv;
vector<pair<long long, long long> > pw;
bool flag;
bool ok[100005];
long long se[100005];
long long see[100005];
long long me[100005];
int main() {
  ios_base::sync_with_stdio(false);
  cin >> n >> k;
  long long c = 1;
  long long h = 3;
  for (int i = 1; i <= k; i++) {
    c += h;
    h *= 3;
    if (n < c) {
      cout << "No";
      return 0;
    }
  }
  for (int i = 1; i < n; i++) {
    cin >> x >> y;
    v[x].push_back(y);
    v[y].push_back(x);
  }
  for (int i = 1; i <= n; i++) {
    se[i] = v[i].size();
    see[i] = se[i];
  }
  k++;
  for (int i = 1; i <= n; i++) {
    if (v[i].size() == 0 || v[i].size() == 2) {
      cout << "NO";
      return 0;
    }
    if (v[i].size() == 1) {
      ok[i] = true;
      se[v[i][0]]--;
    }
  }
  for (int i = 1; i <= n; i++) {
    if (see[i] != se[i] && see[i] < se[i] + 3 && !ok[i]) {
      cout << "No";
      return 0;
    }
    see[i] = se[i];
  }
  k--;
  while (k > 1) {
    for (int i = 1; i <= n; i++) {
      if (!ok[i]) {
        if (see[i] == 0 || see[i] == 2) {
          if (see[i] == 0 && k == 1) {
            ok[i] = true;
            for (int j = 1; j <= n; j++) {
              if (!ok[j]) {
                cout << "No";
                return 0;
              }
            }
            cout << "Yes";
            return 0;
          }
          cout << "No";
          return 0;
        }
        if (see[i] == 1) {
          ok[i] = true;
          for (auto p : v[i]) {
            se[p]--;
          }
        }
      }
    }
    for (int i = 1; i <= n; i++) {
      if (see[i] != se[i] && see[i] < se[i] + 3 && !ok[i]) {
        cout << "No";
        return 0;
      }
      see[i] = se[i];
    }
    k--;
  }
  for (int i = 1; i <= n; i++) {
    if (!ok[i]) {
      if (flag) {
        cout << "No";
        return 0;
      }
      flag = true;
    }
  }
  cout << "Yes";
}
