GCD on Tree
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## Algorithms, Regular expression, String, Trees

Problem
Editorial
Analytics

Given a tree with $N$ vertices. Each vertex has a value $a_i$. For vertex $i$ and $j$, if some vextex $x$ is on the path between $i$ and $j$, and $x$ is neither $i$ nor $j$, we update $Ans_x=max(Ans_x,GCD(a_i,a_j))$$GCD$ means the greatest common divisor function. $Ans$ is an array of $N$ zeros initial.

Find the $Ans$ array after all updation.

## Input Format

First line contains an integer $N(1\le N\le 10^5)$.

Second line contains $N$ integers, represent the array $a(1\le a_i\le 10^5)$.

Each of the next $N-1$ lines contains two integers $u,v$, represent an edge in the tree.

## Output Format

$N$ integers in one line, represent the array $Ans$, separated by space.

SAMPLE INPUT
7
2 1 6 1 6 1 3
1 2
2 3
3 4
4 5
3 6
6 7

SAMPLE OUTPUT
0 2 3 6 0 3 0

Explanation

Vertex $2$ is updated by $1$ and $5$,

Vertex $3,6$ is updated by $5$ and $7$,

Vertex $4$ is updated by $3$ and $5$,

Time Limit: 3.0 sec(s) for each input file.
Memory Limit: 256 MB
Source Limit: 1024 KB

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