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<int> G[2 * 100000 + 5];
int par[2 * 100000 + 5];
std::vector<pair<int, int>> edges;
int alive[100000 + 2];
int deg[100000 + 2];
int N, K;
int ok = 1;
void deal(int u, int v, map<int, int> &new_leaves, vector<int> &cut) {
  if (deg[u] == 1 and alive[v] == 1) {
    new_leaves[v]++;
    cut.push_back(u);
    cut.push_back(v);
  }
}
bool reduce() {
  std::map<int, int> new_leaves;
  std::vector<int> cut;
  for (const auto &e : edges) {
    int u = e.first;
    int v = e.second;
    deal(u, v, new_leaves, cut);
    deal(v, u, new_leaves, cut);
  }
  for (int c : cut) {
    deg[c]--;
    if (deg[c] == 0) alive[c] = 0;
  }
  for (auto nl : new_leaves) {
    if (deg[nl.first] > 1 or nl.second < 3) return false;
    alive[nl.first] = 1;
  }
  return true;
}
int main() {
  cin >> N >> K;
  for (int i = 1; i < N; ++i) {
    int u, v;
    scanf("%d", &u);
    scanf("%d", &v);
    G[u].push_back(v);
    G[v].push_back(u);
    edges.push_back({u, v});
    deg[u]++;
    deg[v]++;
  }
  for (int i = 1; i <= N; ++i) alive[i] = 1;
  int k = 0;
  while (reduce()) {
    ++k;
    int all = 0;
    for (int i = 1; i <= N; ++i) all += alive[i];
    if (all <= 1) break;
  }
  int all = 0;
  for (int i = 1; i <= N; ++i) all += alive[i];
  printf(N > 3 and all == 1 and k == K ? "Yes" : "No");
}
