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;
inline void print(int n) {
  if (n == 0) {
    putchar('0');
    putchar('\n');
  } else if (n == -1) {
    putchar('-');
    putchar('1');
    putchar('\n');
  } else {
    char buf[11];
    buf[10] = '\n';
    int i = 9;
    while (n) {
      buf[i--] = n % 10 + '0';
      n /= 10;
    }
    while (buf[i] != '\n') putchar(buf[++i]);
  }
}
int read() {
  int cc = getc(stdin);
  for (; cc < '0' || cc > '9';) cc = getc(stdin);
  int ret = 0;
  for (; cc >= '0' && cc <= '9';) {
    ret = ret * 10 + cc - '0';
    cc = getc(stdin);
  }
  return ret;
}
long long power(long long num, long long g) {
  if (g == 0) return 1;
  if (g % 2 == 1) return (num * power((num * num), g / 2));
  return power((num * num), g / 2);
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int n, k;
  cin >> n >> k;
  vector<int> vec[n + 1];
  for (int i = 0; i < n - 1; i++) {
    int u, v;
    cin >> u >> v;
    vec[u].push_back(v);
    vec[v].push_back(u);
  }
  int g = 0, re = -1;
  for (int i = 0; i < n; i++) {
    if (vec[i + 1].size() == 2)
      g = 2;
    else if (vec[i + 1].size() == 3)
      g++, re = i + 1;
  }
  if (g > 1) {
    cout << "NO\n";
    return 0;
  }
  queue<int> q;
  bool visit[n + 1];
  memset(visit, false, sizeof(visit));
  for (int i = 0; i < n; i++) {
    if (vec[i + 1].size() == 1) {
      q.push(i + 1);
      visit[i + 1] = true;
    }
  }
  if (k > n) {
    cout << "NO\n";
    return 0;
  }
  int yu = k;
  while (k--) {
    int l = q.size();
    while (l--) {
      int h = q.front();
      int p = 0;
      q.pop();
      for (int i = 0; i < vec[h].size(); i++) {
        if (visit[vec[h][i]]) continue;
        p++;
        visit[vec[h][i]] = true;
        q.push(vec[h][i]);
      }
      if (p > 1) {
        cout << "NO\n";
        return 0;
      }
    }
  }
  if (q.size() == 1) {
    if (re > -1 && re != q.front()) {
      cout << "NO\n";
      return 0;
    }
    bool is = false;
    memset(visit, false, sizeof(visit));
    visit[q.front()] = true;
    while (yu--) {
      int l = q.size();
      while (l--) {
        g = q.front();
        q.pop();
        if (yu > 0 && vec[g].size() == 1) {
          cout << "NO\n";
          return 0;
        }
        for (int i = 0; i < vec[g].size(); i++) {
          if (visit[vec[g][i]]) continue;
          q.push(vec[g][i]);
          visit[vec[g][i]] = true;
        }
      }
    }
    while (!q.empty()) {
      if (vec[q.front()].size() > 1) {
        cout << "NO\n";
        return 0;
      }
      q.pop();
    }
    cout << "YES\n";
    return 0;
  }
  cout << "NO\n";
  return 0;
}
