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;
template <typename T>
T id(T b) {
  return b;
};
template <class It>
bool all(It f, It l) {
  return std::all_of(f, l, id<bool>);
}
template <class It>
bool any(It f, It l) {
  return std::any_of(f, l, id<bool>);
}
template <typename T>
void chmax(T &x, T y) {
  if (x < y) x = y;
}
template <typename T>
void chmin(T &x, T y) {
  if (x > y) x = y;
}
void fastio() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
}
const int MAX_N = 100000;
int n, k;
vector<int> g[MAX_N];
bool vis[MAX_N];
int p[MAX_N];
int d[MAX_N];
int c[MAX_N];
int main() {
  cin >> n >> k;
  for (int i = 0; i < int(n - 1); i++) {
    int u, v;
    cin >> u >> v;
    u--, v--;
    g[u].push_back(v);
    g[v].push_back(u);
  }
  fill_n(p, n, -1);
  bool ok = true;
  queue<int> q;
  for (int i = 0; i < int(n); i++) {
    if (g[i].size() == 1) {
      q.push(i);
      vis[i] = true;
    }
  }
  while (!q.empty()) {
    int u = q.front();
    q.pop();
    for (int v : g[u]) {
      if (p[v] == u) continue;
      ok &= p[u] < 0;
      p[u] = v;
      c[v]++;
      if (!vis[v]) {
        d[v] = d[u] + 1;
        q.push(v);
        vis[v] = true;
      }
      ok &= d[v] == d[u] + 1;
    }
  }
  int mi = max_element(d, d + n) - d;
  ok &= d[mi] == k;
  for (int i = 0; i < int(n); i++) {
    ok &= c[i] >= 3 || (g[i].size() == 1 && c[i] == 0);
  }
  if (ok)
    cout << "Yes\n";
  else
    cout << "No\n";
  return 0;
}
