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 N = 1e5 + 10;
int start;
int d[N];
vector<int> adj[N];
void dfs(int v, int par, int depth) {
  d[v] = depth;
  for (auto u : adj[v])
    if (u != par) {
      dfs(u, v, depth + 1);
    }
}
void done(bool res = false) {
  if (res)
    puts("Yes");
  else
    puts("No");
  exit(0);
}
int center = -1;
bool get_center(int cur, int par, int target, int rem) {
  if (cur == target) return 1;
  for (auto u : adj[cur])
    if (u != par) {
      if (get_center(u, cur, target, rem - 1)) {
        if (rem == 0) center = cur;
        return true;
      }
    }
  return false;
}
int main() {
  int n, k;
  scanf("%d %d", &n, &k);
  for (int i = 0; i < n - 1; i++) {
    int x, y;
    scanf("%d %d", &x, &y);
    x--, y--;
    adj[x].push_back(y);
    adj[y].push_back(x);
  }
  while (adj[start].size() > 1) start++;
  dfs(start, -1, 0);
  int mx_dist = 0;
  int mx_dist_idx = 0;
  for (int i = 0; i < n; i++) {
    mx_dist = max(mx_dist, d[i]);
    if (mx_dist == d[i]) mx_dist_idx = i;
  }
  if (mx_dist != 2 * k) done();
  get_center(start, -1, mx_dist_idx, k);
  dfs(center, -1, 0);
  for (int i = 0; i < n; i++)
    if (adj[i].size() == 1) {
      if (d[i] != k) done();
    }
  for (int i = 0; i < n; i++)
    if (i != center) {
      if (adj[i].size() > 1) {
        if (adj[i].size() <= 3) done();
      }
    }
  if (adj[center].size() < 3) done();
  done(true);
  return 0;
}
