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 <class X, class Y>
void amin(X& x, const Y& y) {
  if (x > y) x = y;
}
template <class X, class Y>
void amax(X& x, const Y& y) {
  if (x < y) x = y;
}
const int INF = 1e9 + 10;
const long long INFL = (long long)1e18 + 10;
const int MAX = 1e5 + 10;
int n, k;
vector<int> es[MAX];
int par[MAX], h[MAX];
void yes() {
  cout << "Yes";
  exit(0);
}
void no() {
  cout << "No";
  exit(0);
}
void visit(int u) {
  for (auto v : es[u])
    if (v != par[u]) {
      par[v] = u;
      h[v] = h[u] + 1;
      visit(v);
    }
}
bool check(int u, int p, int k) {
  if ((int((es[u]).size())) == 1) return k == 0;
  if (k == 0) return false;
  if (p != 0 && (int((es[u]).size())) <= 3) return false;
  for (auto v : es[u])
    if (v != p) {
      if (!check(v, u, k - 1)) return false;
    }
  return true;
}
void process() {
  cin >> n >> k;
  for (int i = 1; i < n; i++) {
    int u, v;
    cin >> u >> v;
    es[u].push_back(v);
    es[v].push_back(u);
  }
  for (int i = 1; i <= n; i++)
    if ((int((es[i]).size())) == 2) no();
  int root = 0;
  for (int i = 1; i <= n; i++)
    if ((int((es[i]).size())) == 1) {
      visit(i);
      int mv = i;
      for (int j = 1; j <= n; j++)
        if (h[j] > h[mv]) mv = j;
      if (h[mv] != 2 * k) no();
      while (h[mv] != k) mv = par[mv];
      root = mv;
      break;
    }
  if (root == 0) no();
  if (check(root, 0, k))
    yes();
  else
    no();
}
int main() {
  ios_base::sync_with_stdio(false);
  process();
}
