# You Are Given a Tree

## 题目描述

A tree is an undirected graph with exactly one simple path between each pair of vertices. We call a set of simple paths $k$ -valid if each vertex of the tree belongs to no more than one of these paths (including endpoints) and each path consists of exactly $k$ vertices. You are given a tree with $n$ vertices. For each $k$ from $1$ to $n$ inclusive find what is the maximum possible size of a $k$ -valid set of simple paths.

## 输入输出格式

### 输入格式

The first line of the input contains a single integer $n$ ( $2 \le n \le 100\,000$ ) — the number of vertices in the tree. Then following $n - 1$ lines describe the tree, each of them contains two integers $v$ , $u$ ( $1 \le v, u \le n$ ) — endpoints of the corresponding edge. It is guaranteed, that the given graph is a tree.

### 输出格式

Output $n$ numbers, the $i$ -th of which is the maximum possible number of paths in an $i$ -valid set of paths.

## 输入输出样例

### 输入样例 #1

7
1 2
2 3
3 4
4 5
5 6
6 7


### 输出样例 #1

7
3
2
1
1
1
1



### 输入样例 #2

6
1 2
2 3
2 4
1 5
5 6


### 输出样例 #2

6
2
2
1
1
0



## 说明

One way to achieve the optimal number of paths for the second sample is illustrated in the following picture: ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF1039D/e329fedb3b5635727a2fc3d6daa41da197dc92a6.png)