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;
int n, Dis[100000 + 5], Fa[100000 + 5], d;
long long int k;
vector<int> Vec[100000 + 5];
void dfs(int z, int fa, int dep) {
  Dis[z] = dep, Fa[z] = fa;
  for (int d : Vec[z])
    if (d != fa) dfs(d, z, dep + 1);
}
int FindCenter() {
  dfs(1, 0, 0);
  int Max = 1;
  for (int i = 2; i <= n; i++)
    if (Dis[i] > Dis[Max]) Max = i;
  for (int i = 1; i <= n; i++) Dis[i] = 0;
  dfs(Max, 0, 0);
  for (int i = 1; i <= n; i++)
    if (Dis[i] > Dis[Max]) Max = i;
  d = Dis[Max];
  int rt = Max;
  if (d & 1) return -1;
  for (int r = d >> 1; r; r--) rt = Fa[rt];
  return rt;
}
int main() {
  scanf("%d%d", &n, &k);
  vector<int> deg(n + 1, 0);
  for (int i = 1, u, v; i < n; i++) {
    scanf("%d%d", &u, &v);
    Vec[u].push_back(v);
    deg[u]++;
    Vec[v].push_back(u);
    deg[v]++;
  }
  int rt = FindCenter();
  if (rt == -1)
    puts("No");
  else {
    for (int i = 1; i <= n; i++) Dis[i] = 0;
    dfs(rt, 0, 0);
    int flg = 1;
    if (!(k == d / 2)) {
      puts("No");
      flg = 0;
    }
    if (flg) {
      bool ok = true;
      for (int i = 1; i <= n; i++) {
        if (i == rt) {
          if (deg[i] <= 2) ok = false;
        } else if (Dis[i] < d / 2) {
          if (deg[i] <= 3) ok = false;
        } else if (Dis[i] == d / 2) {
          if (deg[i] != 1) k = false;
        }
      }
      puts(ok ? "Yes" : "No");
    }
  }
  return 0;
}
