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 = 100005;
struct node {
  int to, next;
} edge[MAXN * 2];
int head[MAXN], top = 0;
inline void push(int i, int j) {
  edge[++top] = (node){j, head[i]}, head[i] = top;
}
int n, k;
int u, v;
int d[MAXN], fa[MAXN];
int depth[MAXN];
void dfs(int nd, int f) {
  if (f == 0) depth[nd] = 0;
  fa[nd] = f;
  for (int i = head[nd]; i; i = edge[i].next) {
    int to = edge[i].to;
    if (to == f) continue;
    depth[to] = depth[nd] + 1;
    dfs(to, nd);
  }
}
int go_up(int nd, int k) {
  if (k > n) {
    puts("No");
    exit(0);
  }
  for (int i = 1; i <= k; i++) nd = fa[nd];
  return nd;
}
int main() {
  scanf("%d%d", &n, &k);
  if (n < 4) {
    puts("No");
    return 0;
  }
  for (int i = 1; i < n; i++) {
    scanf("%d%d", &u, &v);
    push(u, v), push(v, u);
    d[u]++, d[v]++;
  }
  static int stk[MAXN];
  int top = 0;
  for (int i = 1; i <= n; i++)
    if (d[i] == 1) stk[++top] = i;
  if (top < 2) {
    puts("No");
    return 0;
  }
  dfs(stk[1], 0);
  int center = -1;
  for (int i = 2; i <= top; i++)
    if (depth[stk[i]] == 2 * k) {
      center = go_up(stk[i], k);
      break;
    }
  if (center == -1) {
    puts("No");
    return 0;
  }
  dfs(center, 0);
  for (int i = 1; i <= top; i++)
    if (depth[stk[i]] != k) {
      puts("No");
      return 0;
    }
  if (d[center] < 3) {
    puts("No");
    return 0;
  }
  for (int i = 1; i <= n; i++) {
    if (d[i] == 1 || i == center) continue;
    if (d[i] < 4) {
      puts("No");
      return 0;
    }
  }
  puts("Yes");
  return 0;
}
