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 <typename T>
void read(T &x) {
  x = 0;
  char ch = getchar();
  int f = 1;
  while (!isdigit(ch)) {
    if (ch == '-') f *= -1;
    ch = getchar();
  }
  while (isdigit(ch)) {
    x = x * 10 + ch - 48;
    ch = getchar();
  }
  x *= f;
}
int n, k, u, v, md, dep, st[100010], stn = 0, rt, ok = 1;
vector<int> G[100010];
void dfs(int num, int fa, int cd) {
  if (cd > md) {
    dep = num;
    md = cd;
  }
  for (auto ct : G[num]) {
    if (ct == fa) continue;
    dfs(ct, num, cd + 1);
  }
}
void dfsfnd(int num, int fa) {
  st[stn++] = num;
  if (num == dep) rt = st[md / 2];
  for (auto ct : G[num]) {
    if (ct == fa) continue;
    dfsfnd(ct, num);
  }
  stn--;
}
void validate(int num, int fa, int k) {
  if (k == 0) {
    if (G[num].size() != 1) ok = 0;
    return;
  }
  if (G[num].size() - (fa != -1) < 3) ok = 0;
  for (auto ct : G[num]) {
    if (ct == fa) continue;
    validate(ct, num, k - 1);
  }
}
int main() {
  read(n);
  read(k);
  for (int i = 1; i < n; i++) {
    read(u);
    read(v);
    G[u].push_back(v);
    G[v].push_back(u);
  }
  md = -1;
  dfs(1, -1, 0);
  int cc = dep, dd;
  md = -1;
  dfs(cc, -1, 0);
  dd = dep;
  if (md % 2) {
    cout << "No" << endl;
    return 0;
  }
  dfsfnd(cc, -1);
  validate(rt, -1, k);
  if (ok) {
    cout << "Yes" << endl;
  } else {
    cout << "No" << endl;
  }
  return 0;
}
