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;
static long long gcd(long long x, long long y) {
  return 0 == y ? x : gcd(y, x % y);
}
static long long powm(long long x, long long n, long long m) {
  long long r = 1;
  while (n > 0) {
    if (n & 1) r = r * x % m;
    x = x * x % m;
    n /= 2;
  }
  return r;
}
static const long long mod = 998244353;
void no() {
  puts("No");
  exit(0);
}
void yes() {
  puts("Yes");
  exit(0);
}
int N, K;
vector<int> g[1 << 17];
int deg[1 << 17];
int chil[1 << 17];
int color[1 << 17];
int solve() {
  scanf("%d%d", &N, &K);
  if (K > 10) {
    no();
  }
  for (int i = (1), __b = (N - 1); i <= __b; ++i) {
    int x, y;
    scanf("%d%d", &x, &y);
    g[x].push_back(y);
    g[y].push_back(x);
    deg[x]++;
    deg[y]++;
  }
  for (int i = (1), __b = (N); i <= __b; ++i) color[i] = 1;
  int rem_cnt = 0;
  for (int step = (1), __b = (K); step <= __b; ++step) {
    bool fl = false;
    vector<int> d, e;
    set<int> ss;
    for (int i = (1), __b = (N); i <= __b; ++i) {
      if (deg[i] == 1) {
        d.push_back(i);
        color[i] = 0;
      }
    }
    fl = d.size() > 0;
    if (!fl) {
      no();
    }
    rem_cnt += d.size();
    for (int x : d) {
      int y = g[x][0];
      if (color[y] == 0) no();
      deg[x]--;
      deg[y]--;
      chil[y]++;
      ss.insert(y);
    }
    if (step == K) {
      if (ss.size() != 1) no();
      int root = *ss.begin();
      for (int i = (1), __b = (N); i <= __b; ++i) {
        if (deg[i] == 0 && color[i] == 1) e.push_back(i);
      }
      if (e.size() == 1 && root == e[0] && chil[root] >= 3)
        yes();
      else
        no();
    }
    for (int i = (1), __b = (N); i <= __b; ++i) {
      if (deg[i] == 1) {
        e.push_back(i);
      }
    }
    fl = e.size() > 0;
    if (!fl) {
      no();
    }
    vector<int> w(ss.begin(), ss.end());
    if (e != w) {
      no();
    }
    for (int x : e) {
      if (chil[x] < 3) no();
      int pa = 0;
      for (int y : g[x]) {
        if (color[y] != 0) pa = y;
      }
      if (pa == 0) no();
      g[x].clear();
      g[x].push_back(pa);
    }
  }
  if (rem_cnt != N - 1) no();
  yes();
  return 0;
}
int main() {
  ::std::ios::sync_with_stdio(false);
  ::std::cin.tie(0);
  ::std::cout.tie(0);
  int t = 1;
  while (t--) solve();
}
