#include <bits/stdc++.h>
const int N = 1e5 + 1;
std::set<int> adj[N];
int main() {
  int n, k;
  scanf("%d%d", &n, &k);
  for (int i = 1; i < n; ++i) {
    int u, v;
    scanf("%d%d", &u, &v);
    adj[u].insert(v);
    adj[v].insert(u);
  }
  bool found_center = false;
  int center = 0;
  std::set<int> leaf;
  for (int i = 1; i <= n; ++i)
    if (adj[i].size() == 2) {
      printf("No");
      return 0;
    } else if (adj[i].size() == 3)
      if (!found_center) {
        found_center = true;
        center = i;
      } else {
        printf("No");
        return 0;
      }
    else if (adj[i].size() == 1)
      leaf.insert(i);
  for (int i = 1; i <= k; ++i) {
    std::set<int> parent;
    for (int u : leaf)
      if (adj[u].size() != 1) {
        printf("No");
        return 0;
      }
    for (int u : leaf) {
      int v = *adj[u].begin();
      adj[v].erase(u);
      parent.insert(v);
    }
    std::swap(leaf, parent);
  }
  if (leaf.size() != 1) {
    printf("No");
    return 0;
  }
  int last = *leaf.begin();
  if (!found_center || last == center)
    printf("Yes");
  else
    printf("No");
  return 0;
}

### Prompt

In Cpp, your task is to solve the following problem:

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.

### Response

```cpp
#include <bits/stdc++.h>
const int N = 1e5 + 1;
std::set<int> adj[N];
int main() {
  int n, k;
  scanf("%d%d", &n, &k);
  for (int i = 1; i < n; ++i) {
    int u, v;
    scanf("%d%d", &u, &v);
    adj[u].insert(v);
    adj[v].insert(u);
  }
  bool found_center = false;
  int center = 0;
  std::set<int> leaf;
  for (int i = 1; i <= n; ++i)
    if (adj[i].size() == 2) {
      printf("No");
      return 0;
    } else if (adj[i].size() == 3)
      if (!found_center) {
        found_center = true;
        center = i;
      } else {
        printf("No");
        return 0;
      }
    else if (adj[i].size() == 1)
      leaf.insert(i);
  for (int i = 1; i <= k; ++i) {
    std::set<int> parent;
    for (int u : leaf)
      if (adj[u].size() != 1) {
        printf("No");
        return 0;
      }
    for (int u : leaf) {
      int v = *adj[u].begin();
      adj[v].erase(u);
      parent.insert(v);
    }
    std::swap(leaf, parent);
  }
  if (leaf.size() != 1) {
    printf("No");
    return 0;
  }
  int last = *leaf.begin();
  if (!found_center || last == center)
    printf("Yes");
  else
    printf("No");
  return 0;
}

```