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> ga[100005];
int in[100001][16], vis[100001], x, y, i, j, s, k, n, p;
int main() {
  cin >> n >> k;
  for (i = 1; i <= n - 1; i++) {
    cin >> x >> y;
    ga[x].push_back(y);
    ga[y].push_back(x);
    in[x][0]++;
    in[y][0]++;
  }
  if (k >= 15 || n <= 3)
    cout << "No";
  else {
    s = n;
    for (p = 1; p <= k; p++) {
      for (i = 1; i <= n; i++)
        if (in[i][p - 1] == 1) {
          for (j = 0; j < ga[i].size(); j++) {
            if (vis[ga[i][j]]) continue;
            if (vis[ga[i][j]] == 0 && in[ga[i][j]][p - 1] == 1) {
              cout << "No";
              return 0;
            }
            in[ga[i][j]][p]++;
          }
          vis[i] = 1;
          s--;
        }
      for (i = 1; i <= n; i++) {
        if (in[i][p] == 0 || vis[i]) continue;
        if (in[i][p] <= 2) {
          cout << "No";
          return 0;
        }
        in[i][p] = 1;
      }
      if (s == 1) {
        if (p == k)
          cout << "Yes";
        else
          cout << "No";
        return 0;
      }
    }
    cout << "No";
    return 0;
  }
}
