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;
int main() {
  int n, m;
  cin >> n >> m;
  auto no_solution = [&]() {
    cout << "No" << endl;
    exit(0);
  };
  if (n == 1) {
    no_solution();
  }
  vector<vector<int>> adj(n);
  for (int i = 0; i < n - 1; ++i) {
    int x, y;
    cin >> x >> y;
    --x;
    --y;
    adj[x].push_back(y);
    adj[y].push_back(x);
  }
  int s = -1;
  for (int i = 0; i < n; ++i) {
    if (adj[i].size() == 1) {
      s = i;
      break;
    }
  }
  vector<int> depth(n, 0), parent(n, -1);
  function<void(int)> dfs = [&](int x) {
    for (auto y : adj[x]) {
      if (y != parent[x]) {
        depth[y] = depth[x] + 1;
        parent[y] = x;
        dfs(y);
      }
    }
  };
  dfs(s);
  int t = max_element(depth.begin(), depth.end()) - depth.begin();
  if (depth[t] < m) {
    no_solution();
  }
  function<void(int, int)> solve = [&](int x, int parent) {
    int size = 0;
    for (auto y : adj[x]) {
      if (y != parent) {
        depth[y] = depth[x] + 1;
        solve(y, x);
        ++size;
      }
    }
    if (!size) {
      if (depth[x] != m) {
        no_solution();
      }
    } else if (size < 3) {
      no_solution();
    }
  };
  for (int i = 0; i < m; ++i) {
    t = parent[t];
  }
  depth[t] = 0;
  solve(t, -1);
  cout << "Yes" << endl;
  return 0;
}
