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;
const int MAX_N = 100 * 1000;
int n, k;
array<vector<int>, MAX_N> edges;
int getCentre() {
  vector<int> degree(n, 0);
  int done = 0;
  vector<int> thisLevel;
  vector<int> nextLevel;
  for (int i = 0; i < n; ++i)
    for (const auto& son : edges[i]) degree[son]++;
  for (int i = 0; i < n; ++i)
    if (degree[i] == 1) thisLevel.push_back(i), degree[i] = 0;
  while (done + 2 < n) {
    done += thisLevel.size();
    for (const auto& x : thisLevel)
      for (const auto& son : edges[x])
        if (degree[son] > 2)
          degree[son] -= 1;
        else if (degree[son] == 2)
          nextLevel.push_back(son), degree[son] = 0;
    swap(thisLevel, nextLevel);
    nextLevel.clear();
  }
  if (thisLevel.size() == 1) return thisLevel[0];
  return -1;
}
pair<int, int> minMaxDepth(int me, int dad) {
  if (edges[me].size() == 1) return {1, 1};
  pair<int, int> ans(-1, -1);
  for (const auto& son : edges[me])
    if (son != dad) {
      auto res = minMaxDepth(son, me);
      if (ans.first == -1 && ans.second == -1)
        ans.first = res.first + 1, ans.second = res.second + 1;
      else
        ans.first = min(ans.first, res.first + 1),
        ans.second = max(ans.second, res.second + 1);
    }
  return ans;
}
bool atLeast3Sons(int me, int dad) {
  if (edges[me].size() == 1) return true;
  if (edges[me].size() < 3) return false;
  if (edges[me].size() < 4 && dad != -1) return false;
  for (const auto& son : edges[me])
    if (son != dad)
      if (!atLeast3Sons(son, me)) return false;
  return true;
}
int main() {
  std::ios::sync_with_stdio(false);
  cin >> n >> k;
  for (int i = 0; i < n - 1; ++i) {
    int a, b;
    cin >> a >> b;
    edges[a - 1].push_back(b - 1);
    edges[b - 1].push_back(a - 1);
  }
  if (n < 4) {
    cout << "No" << endl;
    return 0;
  }
  int centre = getCentre();
  if (centre == -1) {
    cout << "No" << endl;
    return 0;
  }
  auto minMaxD = minMaxDepth(centre, -1);
  if (minMaxD.first != minMaxD.second) {
    cout << "No" << endl;
    return 0;
  }
  if (minMaxD.first - 1 != k) {
    cout << "No" << endl;
    return 0;
  }
  if (!atLeast3Sons(centre, -1)) {
    cout << "No" << endl;
    return 0;
  }
  cout << "Yes" << endl;
  return 0;
}
