SOLVE
LATER
You are given a tree with $$n$$ nodes. The nodes are numbered from $$1$$ to $$n$$. Let us define the gcd of a path as the greatest common divisor of all values of the nodes in the path. Let $$F(g)$$ denote the number of simple paths on the tree whose gcd is $$g$$. Formally, $$F(g)$$ equals the number of sequences $$p_1,p_2, \cdots , p_k$$, such that $$p_i$$ and $$p_{i+1}$$ are connected by an edge for all $$i < k $$, and $$p_i \neq p_j$$ for $$i \neq j$$, and $$gcd(p_1,p_2,\cdots p_k) = g$$.
Find the values of $$F(g)$$ for all $$1 \leq g \leq n $$
Input
The first line contains $$n$$, the number of nodes in the tree.
Each of the next $$n-1$$ lines contain 2 integers $$u,v$$, denoting node $$u$$, and node $$v$$ are connected by an edge.
Output
Print a single line containing $$n$$ integers. The $$i^{\text{th}}$$ integer equals $$F(i)$$.
Constraints
$$1 \le n \le 10^6 $$
The path from $$2$$ to $$4$$, and the path from $$4 $$ to $$2$$, has gcd value 2. All other paths with more than 1 nodes have gcd 1. The path $$i $$ to $$ i$$ has gcd $$i$$