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 const mod = 1e9 + 7;
long long power(long long x, long long y, long long mod = 2e18) {
  long long ans = 1;
  x %= mod;
  while (y) {
    if (y & 1) ans = (x * ans) % mod;
    x = (x * x) % mod;
    y >>= 1;
  }
  return ans;
}
long long gcd(long long a, long long b) {
  if (a == 0) return b;
  return gcd(b % a, a);
}
vector<long long> v[100010];
bool vis[100010];
void No() {
  cout << "No\n";
  exit(0);
}
signed main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  long long n, k;
  cin >> n >> k;
  if (k >= n) {
    cout << "No\n";
    return 0;
  }
  for (long long i = 0; i < n - 1; i++) {
    long long x, y;
    cin >> x >> y;
    v[x].push_back(y);
    v[y].push_back(x);
  }
  queue<pair<long long, long long>> q;
  for (long long i = 1; i <= n; i++) {
    if (v[i].size() == 1) {
      q.push({i, 0});
    }
  }
  long long cen = -1;
  while (q.size()) {
    pair<long long, long long> p = q.front();
    q.pop();
    if (vis[p.first]) continue;
    vis[p.first] = 1;
    if (p.second == k) {
      cen = p.first;
      break;
    }
    for (auto x : v[p.first]) {
      if (!vis[x]) q.push({x, p.second + 1});
    }
  }
  memset(vis, 0, sizeof(vis));
  queue<pair<long long, long long>> Q;
  Q.push({cen, 0});
  if (v[cen].size() < 3) {
    No();
  }
  while (Q.size()) {
    pair<long long, long long> p = Q.front();
    Q.pop();
    if (vis[p.first]) continue;
    vis[p.first] = 1;
    if (p.second == k + 1 || (v[p.first].size() == 1 && p.second != k) ||
        (v[p.first].size() < 4 && v[p.first].size() != 1 && p.first != cen)) {
      No();
    }
    for (auto x : v[p.first]) {
      if (!vis[x]) {
        Q.push({x, p.second + 1});
      }
    }
  }
  cout << "Yes\n";
  return 0;
}
