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 = 100111, inf = 1000111222;
int n, k, sz[max_n], h[max_n];
vector<int> g[max_n];
int get_root() {
  queue<int> q;
  for (int i = 1; i <= n; ++i) {
    if (g[i].size() == 1) {
      q.push(i);
    }
    sz[i] = g[i].size();
  }
  int root = 1;
  while (!q.empty()) {
    int v = q.front();
    q.pop();
    root = v;
    for (int to : g[v]) {
      --sz[to];
      if (sz[to] == 1) {
        q.push(to);
      }
    }
  }
  return root;
}
void dfs(int v, int p) {
  int cnt = 0;
  for (int to : g[v]) {
    if (to != p) {
      ++cnt;
      h[to] = h[v] + 1;
      dfs(to, v);
    }
  }
  if (cnt != 0 && cnt < 3) {
    puts("No");
    exit(0);
  }
}
int main() {
  scanf("%d%d", &n, &k);
  if (n == 1) {
    puts("No");
    return 0;
  }
  for (int i = 1; i < n; ++i) {
    int u, v;
    scanf("%d%d", &u, &v);
    g[u].push_back(v);
    g[v].push_back(u);
  }
  int root = get_root();
  dfs(root, -1);
  for (int i = 1; i <= n; ++i) {
    if (g[i].size() == 1 && h[i] != k) {
      puts("No");
      return 0;
    }
  }
  puts("Yes");
  return 0;
}
