A11979. You Are Given a Tree

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.

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