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 T>
using VV = vector<vector<T>>;
template <class T>
inline T SMIN(T& a, const T b) {
  return a = (a > b) ? b : a;
}
template <class T>
inline T SMAX(T& a, const T b) {
  return a = (a < b) ? b : a;
}
template <class Iter>
void dumpc(Iter begin, Iter end) {
  if (false) {
    for (; begin != end; ++begin) {
      cerr << *begin << ',';
    }
    cerr << endl;
  }
}
const int MAX_N = 1e5 + 1;
int N, K;
vector<int> G[MAX_N];
int viz[MAX_N];
void end() {
  cout << "No" << endl;
  exit(0);
}
void dfs(int u, int pre, int d) {
  assert(d <= K);
  if (d == K) {
    assert(int((G[u]).size()) == 1 && G[u][0] == pre);
  } else {
    int children = pre == -1 ? int((G[u]).size()) : int((G[u]).size()) - 1;
    if (children < 3) {
      if (false) {
        cerr << "u"
             << " = " << (u) << ", "
             << "SZ(G[u])"
             << " = " << (int((G[u]).size())) << endl;
      };
      end();
    }
  }
  for (auto& v : G[u])
    if (v != pre) dfs(v, u, d + 1);
}
void solve() {
  queue<int> Q;
  for (int i = 0; i < (N); ++i)
    if (int((G[i]).size()) == 1) Q.emplace(i), viz[i] = 1;
  int step = 0;
  while (step < K) {
    int L = int((Q).size());
    unordered_set<int> vsnext, vscur;
    if (L == 0) {
      if (false) {
        cerr << "step"
             << " = " << (step) << endl;
      };
      end();
    }
    for (int _ = 0; _ < (L); ++_) {
      int u = Q.front();
      Q.pop();
      vscur.emplace(u);
      int par = -1, cnt = 0;
      for (auto& v : G[u]) {
        if (viz[v] == 1) end();
        if (viz[v] == 0) par = v, ++cnt;
      }
      if (par == -1) end();
      if (cnt != 1) end();
      assert(cnt == 1);
      if (vsnext.count(par) == 0) {
        vsnext.emplace(par), Q.emplace(par);
      }
    }
    for (auto& u : vscur) viz[u] = 2;
    for (auto& v : vsnext) viz[v] = 1;
    ++step;
  }
  if (int((Q).size()) != 1) end();
  int c = Q.front();
  viz[c] = 2;
  for (int i = 0; i < (N); ++i) assert(viz[i] == 2);
  dfs(c, -1, 0);
  cout << "Yes" << endl;
}
vector<int> center() {
  vector<int> deg(N, 0);
  queue<int> Q;
  for (int u = 0; u < (N); ++u) {
    int x = int((G[u]).size());
    deg[u] = x;
    if (x == 1) Q.emplace(u);
  }
  while (int((Q).size()) > 2) {
    int L = int((Q).size());
    for (int _ = 0; _ < (L); ++_) {
      int u = Q.front();
      Q.pop();
      --deg[u];
      for (auto& v : G[u]) {
        deg[v]--;
        if (deg[v] == 1) Q.emplace(v);
      }
    }
  }
  vector<int> res;
  while (int((Q).size())) res.push_back(Q.front()), Q.pop();
  return res;
}
int cntd[MAX_N];
void dfs2(int u, int pre, int d) {
  if (d > K) end();
  if (d == K) {
    if (int((G[u]).size()) != 1) end();
  } else {
    int children = pre == -1 ? int((G[u]).size()) : int((G[u]).size()) - 1;
    if (children < 3) {
      if (false) {
        cerr << "u"
             << " = " << (u) << ", "
             << "SZ(G[u])"
             << " = " << (int((G[u]).size())) << endl;
      };
      end();
    }
  }
  for (auto& v : G[u])
    if (v != pre) dfs2(v, u, d + 1);
}
void solve_ok() {
  vector<int> cs = center();
  if (int((cs).size()) != 1) end();
  int c = cs.front();
  dfs2(c, -1, 0);
  cout << "Yes" << endl;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cin >> N >> K;
  for (int i = 0; i < (N - 1); ++i) {
    int u, v;
    cin >> u >> v;
    --u, --v;
    G[u].push_back(v), G[v].push_back(u);
  }
  solve();
  return 0;
}
