# #P1039D. You Are Given a Tree

ID: 2578 Type: RemoteJudge 7000ms 512MiB 尝试: 1 已通过: 1 难度: 10 上传者: 标签>data structuresdptrees*2800

# You Are Given a Tree

## Description

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.

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.

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

## Input

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.

## Output

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

## Samples

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

``````
``````7
3
2
1
1
1
1

``````
``````6
1 2
2 3
2 4
1 5
5 6

``````
``````6
2
2
1
1
0

``````

## Note

One way to achieve the optimal number of paths for the second sample is illustrated in the following picture: