# Multihedgehog

## 题意翻译

【题意简述】\ 定义一棵树 k-multihedgehog： 对于 1-multihedgehog，其中一个点度数 \$\ge3\$ ，其它点度数均为 \$1\$. k-multihedgehog 是在 k-1-multihedgehog 的基础上，把所有度为 \$1\$ 的点替换成一个 1-multihedgehog 并与原图相连。

## 题目描述

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 \ge 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.

## 输入输出格式

### 输入格式

First line of input contains \$ 2 \$ integers \$ n \$ , \$ k \$ ( \$ 1 \le n \le 10^{5} \$ , \$ 1 \le k \le 10^{9} \$ ) — number of vertices and hedgehog parameter. Next \$ n-1 \$ lines contains two integers \$ u \$ \$ v \$ ( \$ 1 \le u, \,\, v \le n; \,\, u \ne v \$ ) — indices of vertices connected by edge. It is guaranteed that given graph is a tree.

### 输出格式

Print "Yes" (without quotes), if given graph is \$ k \$ -multihedgehog, and "No" (without quotes) otherwise.

## 输入输出样例

### 输入样例 #1

``````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
``````

### 输出样例 #1

``````Yes
``````

### 输入样例 #2

``````3 1
1 3
2 3
``````

### 输出样例 #2

``````No
``````

## 说明

2-multihedgehog from the first example looks like this: ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF1067B/fa74b226e7f972e84df3729441b7e1df84488eb4.png) 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 \$ .