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;
vector<long long int> adj[100001];
long long int degree[100001];
void addEdge(long long int u, long long int v) {
  adj[u].push_back(v);
  adj[v].push_back(u);
}
int checker(long long int size, long long int k) {
  if (k == 1) {
    long long int counter = 0;
    for (long long int i = 0; i < size; i++) {
      degree[i] = adj[i].size();
      if (degree[i] == 2) return -1;
      if (degree[i] > 1) counter++;
    }
    if (counter != 1) return -1;
    return 0;
  }
  long long int flag = 0;
  for (long long int i = 0; i < size; i++) {
    degree[i] = adj[i].size();
    if (degree[i] == 2) return -1;
  }
  for (long long int i = 0; i < size; i++) {
    flag = 0;
    if (degree[i] == 0) {
      continue;
    }
    if (degree[i] == 1) {
      adj[i].clear();
      continue;
    }
    for (long long int j = 0; j < adj[i].size(); j++) {
      if (degree[adj[i][j]] == 1) {
        flag = 1;
        break;
      }
    }
    if (flag == 0) continue;
    flag = 0;
    long long int deg;
    for (long long int j = 0; j < adj[i].size(); j++) {
      if (degree[adj[i][j]] != 1) {
        flag++;
        deg = j;
      }
    }
    if (flag != 1) return -1;
    adj[i].clear();
    adj[i].push_back(deg);
    if (degree[i] <= 3) return -1;
  }
  return checker(size, k - 1);
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long int n, k;
  cin >> n >> k;
  long long int start, end;
  for (long long int i = 0; i < n - 1; i++) {
    cin >> start >> end;
    start--;
    end--;
    addEdge(start, end);
  }
  if (k >= 12 || n < 4) {
    cout << "No" << endl;
    return 0;
  }
  long long int ans = checker(n, k);
  if (ans != 0) {
    cout << "No" << endl;
  } else {
    cout << "Yes" << endl;
  }
  return 0;
}
