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;
inline long long read() {
  char c = getchar();
  long long u = 0, f = 1;
  while (c != '-' && (c < '0' || '9' < c)) c = getchar();
  if (c == '-') {
    f = -1;
    c = getchar();
  }
  while ('0' <= c && c <= '9') {
    u = u * 10 + c - '0';
    c = getchar();
  }
  return u * f;
}
inline char readc() {
  for (;;) {
    char c = getchar();
    if ('A' <= c && c <= 'Z' || 'a' <= c && c <= 'z') return c;
  }
}
inline int read_digit() {
  for (;;) {
    char c = getchar();
    if ('0' <= c && c <= '9') return c - '0';
  }
}
inline int max(int a, int b) { return a > b ? a : b; }
inline int min(int a, int b) { return a < b ? a : b; }
template <typename T>
inline void updmax(T &a, T b) {
  if (b > a) a = b;
}
template <typename T>
inline void updmin(T &a, T b) {
  if (b < a) a = b;
}
inline void swap(int &a, int &b) {
  int t = a;
  a = b;
  b = t;
}
inline void fileio(string s) {
  if (s == "txt") {
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
  } else {
    freopen((s + ".in").c_str(), "r", stdin);
    freopen((s + ".out").c_str(), "w", stdout);
  }
}
long long Rand(int s = 0, int t = 100000000000000000ll) {
  return rand() % (t - s + 1) + s;
}
void gen(char k) {
  srand(time(NULL));
  string s = "";
  s = s + k;
  ofstream fout("hospital" + s + ".in");
  fout.close();
  return;
}
vector<int> G[200010];
queue<int> cur;
int d[200010], fa[200010], dep[200010], chi[200010];
int maxi = 0;
int main() {
  int n, k;
  n = read();
  k = read();
  for (int i = 1; i < n; i++) {
    int a, b;
    a = read();
    b = read();
    G[a].push_back(b);
    G[b].push_back(a);
    d[a]++;
    d[b]++;
  }
  for (int i = 1; i <= n; i++) {
    if (d[i] == 1) {
      dep[i] = 1;
      cur.push(i);
    }
    if (d[i] == 2) {
      cout << "No" << endl;
      return 0;
    }
  }
  while (!cur.empty()) {
    int k = cur.front();
    cur.pop();
    for (auto u : G[k]) {
      if (dep[u] != 0 && dep[u] != dep[k] + 1 && fa[u] != k) {
        cout << "No" << endl;
        return 0;
      }
      if (dep[u] == 0) {
        dep[u] = dep[k] + 1;
        cur.push(u);
      }
      if (fa[u] != k) {
        fa[k] = u;
        chi[u]++;
      }
    }
  }
  for (int i = 1; i <= n; i++) {
    if (chi[i] == 1 || chi[i] == 2) {
      cout << "No" << endl;
      return 0;
    }
    updmax(maxi, dep[i]);
  }
  if (maxi != k + 1) {
    cout << "No" << endl;
    return 0;
  }
  int cnt = 0;
  for (int i = 1; i <= n; i++) {
    if (dep[i] == maxi) {
      if (cnt == 1) {
        cout << "No" << endl;
        return 0;
      }
      if (chi[i] <= 2) {
        cout << "No" << endl;
        return 0;
      }
      cnt++;
    }
  }
  cout << "Yes" << endl;
  return 0;
}
