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>
std::vector<std::vector<int>> c;
std::vector<int> col;
std::vector<int> p;
std::vector<int> dist;
int curcol = 1;
void dfs(int v) {
  col[v] = curcol;
  for (int i = 0; i < c[v].size(); ++i)
    if (col[c[v][i]] == curcol - 1) {
      p[c[v][i]] = v;
      dist[c[v][i]] = dist[v] + 1;
      dfs(c[v][i]);
    }
}
int main() {
  int n = 0, k = 0;
  std::cin >> n >> k;
  if (n < 4) {
    std::cout << "No\n";
    return 0;
  }
  c.resize(n);
  col.resize(n);
  dist.resize(n);
  p.resize(n);
  for (int i = 0; i < n; ++i) col[i] = 0;
  for (int i = 0; i < n - 1; ++i) {
    int u = 0, v = 0;
    std::cin >> u >> v;
    --v, --u;
    c[v].push_back(u);
    c[u].push_back(v);
  }
  int q = -1;
  for (int i = 0; i < n; ++i)
    if (c[i].size() == 1) {
      q = i;
      break;
    }
  p[q] = -1;
  dist[q] = 0;
  dfs(q);
  bool f = true;
  q = -1;
  for (int i = 0; i < n; ++i) {
    if (dist[i] > 2 * k) {
      f = false;
      break;
    }
    if (dist[i] == 2 * k) {
      q = i;
    }
  }
  if (q == -1 || (!f)) {
    std::cout << "No\n";
    return 0;
  }
  for (int i = 0; i < k; ++i) q = p[q];
  dist[q] = 0;
  curcol++;
  dfs(q);
  for (int i = 0; i < n; ++i) {
    if ((dist[i] == k && c[i].size() != 1) ||
        (dist[i] < k && dist[i] > 0 && c[i].size() < 4) || (dist[i] > k) ||
        (dist[i] == 0 && c[i].size() < 3))
      f = false;
  }
  if (f)
    std::cout << "Yes\n";
  else
    std::cout << "No\n";
}
