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 MAXN = 200 * 1000;
const int INF = 1 << 30;
int N, K;
vector<int> G[MAXN];
vector<int> P, D, Deg;
int MostDistantVertex() {
  int ix = 1;
  for (int i = 1; i <= N; ++i) {
    if (D[i] > D[ix]) {
      ix = i;
    }
  }
  return ix;
}
void BFS(int start) {
  queue<int> q;
  q.push(start);
  D = vector<int>(N + 1, INF);
  P = vector<int>(N + 1);
  Deg = vector<int>(N + 1);
  D[start] = 0;
  while (!q.empty()) {
    int u = q.front();
    q.pop();
    for (int i = 0; i < G[u].size(); ++i) {
      int v = G[u][i];
      if (D[v] == INF) {
        D[v] = D[u] + 1;
        P[v] = u;
        Deg[u]++;
        q.push(v);
      }
    }
  }
}
bool Check() {
  for (int i = 1; i <= N; ++i) {
    if (Deg[i] == 0) {
      if (D[i] != K) {
        return false;
      }
    } else if (Deg[i] < 3) {
      return false;
    }
  }
  return true;
}
int main() {
  scanf("%d %d", &N, &K);
  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);
  }
  BFS(1);
  int u = MostDistantVertex();
  BFS(u);
  int v = MostDistantVertex();
  vector<int> path;
  for (int w = v; w; w = P[w]) {
    path.push_back(w);
  }
  if (path.size() % 2 == 0) {
    cout << "No" << endl;
    return 0;
  }
  int center = path[path.size() / 2];
  BFS(center);
  if (Check())
    cout << "Yes" << endl;
  else
    cout << "No" << endl;
  return 0;
}
