GCD on Tree | Practice Problems

GCD on Tree

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5

4 votes

Regular expression, Hard, Algorithms, String, Trees

Details

Problem

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

Time Limit: 3

Memory Limit: 256

Source Limit:

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 $5$ ,

Contributers:

Niyaz Nigmatullin