write a go solution for 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.

Input Format:
The first line of the input contains a single integer n (2<=n<=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<=v,u<=n) — endpoints of the corresponding edge.

It is guaranteed, that the given graph is a tree.

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

Note:
One way to achieve the optimal number of paths for the second sample is illustrated in the following picture:. Output only the code with no comments, explanation, or additional text.