CF1805D.A Wide, Wide Graph

普及/提高-

通过率：0%

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题目描述

You are given a tree (a connected graph without cycles) with $n$ vertices.

Consider a fixed integer $k$ . Then, the graph $G_k$ is an undirected graph with $n$ vertices, where an edge between vertices $u$ and $v$ exists if and only if the distance between vertices $u$ and $v$ in the given tree is at least $k$ .

For each $k$ from $1$ to $n$ , print the number of connected components in the graph $G_k$ .

输入格式

The first line contains the integer $n$ ( $2 \le n \le 10^5$ ) — the number of vertices in the graph.

Each of the next $n-1$ lines contains two integers $u$ and $v$ ( $1 \le u, v \le n$ ), denoting an edge between vertices $u$ and $v$ in the tree. It is guaranteed that these edges form a valid tree.

输出格式

Output $n$ integers: the number of connected components in the graph $G_k$ for each $k$ from $1$ to $n$ .

输入输出样例

输入#1
```
6
1 2
1 3
2 4
2 5
3 6
```
输出#1
```
1 1 2 4 6 6
```
输入#2
```
5
1 2
2 3
3 4
3 5
```
输出#2
```
1 1 3 5 5
```

说明/提示

In the first example: If $k=1$ , the graph has an edge between each pair of vertices, so it has one component. If $k=4$ , the graph has only edges $4 \leftrightarrow 6$ and $5 \leftrightarrow 6$ , so the graph has $4$ components.

In the second example: when $k=1$ or $k=2$ the graph has one component. When $k=3$ the graph $G_k$ splits into $3$ components: one component has vertices $1$ , $4$ and $5$ , and two more components contain one vertex each. When $k=4$ or $k=5$ each vertex is a separate component.

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