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;
const int maxn = 1e5 + 5;
const int maxm = 2e5 + 5;
const int inf = 1e9;
int head[maxn], ver[maxm], nex[maxm], tot;
void inline AddEdge(int x, int y) {
  ver[++tot] = y, nex[tot] = head[x], head[x] = tot;
}
int n, k;
int d[maxn], dep[maxn], pre[maxn];
bool vis[maxn];
int main() {
  cin >> n >> k;
  for (int i = 0; i < n - 1; i++) {
    int x, y;
    scanf("%d%d", &x, &y);
    AddEdge(x, y);
    AddEdge(y, x);
    d[x]++;
    d[y]++;
  }
  int lf = 0;
  for (int i = 1; i <= n; i++)
    if (d[i] == 1) {
      lf = i;
      break;
    }
  if (!lf) {
    puts("No");
    return 0;
  }
  queue<int> q;
  q.push(lf);
  int rf = 0;
  while (q.size()) {
    int x = q.front();
    q.pop();
    vis[x] = 1;
    for (int i = head[x]; i; i = nex[i]) {
      int y = ver[i];
      if (!vis[y]) {
        dep[y] = dep[x] + 1;
        pre[y] = x;
        q.push(y);
      }
    }
  }
  for (int i = 1; i <= n; i++) {
    if (dep[i] == 2 * k) {
      rf = i;
      break;
    }
  }
  if (!rf) {
    puts("No");
    return 0;
  }
  int rt;
  for (int i = 0; i < k; i++) {
    rf = pre[rf];
  }
  rt = rf;
  memset(vis, 0, sizeof(vis));
  memset(dep, 0, sizeof(dep));
  q.push(rt);
  while (q.size()) {
    int x = q.front();
    q.pop();
    int sum = 0;
    vis[x] = 1;
    for (int i = head[x]; i; i = nex[i]) {
      int y = ver[i];
      if (!vis[y]) {
        dep[y] = dep[x] + 1;
        pre[y] = x;
        q.push(y);
        sum++;
      }
    }
    if (dep[x] < k && sum < 3) {
      puts("No");
      return 0;
    }
    if (dep[x] > k) {
      puts("No");
      return 0;
    }
  }
  puts("Yes");
}
