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;
template <class c>
struct rge {
  c b, e;
};
template <class c>
rge<c> range(c i, c j) {
  return rge<c>{i, j};
}
template <class c>
auto dud(c* x) -> decltype(cerr << *x, 0);
template <class c>
char dud(...);
struct debug {
  template <class c>
  debug& operator<<(const c&) {
    return *this;
  }
};
const int nax = 1e5 + 5;
vector<int> edges[nax];
int degree[nax];
bool removed[nax];
int times[nax];
void NO() {
  puts("NO");
  exit(0);
}
int main() {
  int n, k;
  scanf("%d%d", &n, &k);
  for (int i = 0; i < n - 1; ++i) {
    int a, b;
    scanf("%d%d", &a, &b);
    edges[a].push_back(b);
    edges[b].push_back(a);
    degree[a]++;
    degree[b]++;
  }
  vector<int> q;
  for (int i = 1; i <= n; ++i) {
    if (degree[i] == 1) {
      q.push_back(i);
    }
  }
  for (int rep = 0; rep < k; ++rep) {
    for (int x : q) {
      removed[x] = true;
    }
    if (q.empty()) {
      NO();
    }
    set<int> must, can;
    for (int x : q) {
      for (int y : edges[x]) {
        if (!removed[y]) {
          ++times[y];
          must.insert(y);
          if (--degree[y] == (rep == k - 1 ? 0 : 1)) {
            can.insert(y);
          }
        }
      }
    }
    if (must != can) {
      NO();
    }
    for (int x : must) {
      if (times[x] < 3) {
        NO();
      }
    }
    q.clear();
    for (int x : must) {
      q.push_back(x);
    }
  }
  vector<int> tmp;
  for (int i = 1; i <= n; ++i) {
    if (!removed[i]) {
      tmp.push_back(i);
    }
  }
  if ((int)tmp.size() != 1) {
    NO();
  }
  puts("YES");
}
