Hi , i need help in this question

Problem statement in short :

Given a tree,every node has a value written on it.
There will be several queries of two types:
1 — update value of any node of tree
2 — tell if the product of values of node on path from u to v is divisble by k

All constraints are of order 10^5.

Editorial is not properly explained.
Thanks

I need help in the problem : problem B — center
Someone please share idea on how to solve it.
Thanks

problem B google kickstart

Someone please explain the approach for this problem.

Thanks

Help needed in problem ostap and tree .

Editorial is not understandable.

Thanks

Can someone please proof how number of permutations of first N natural numbers with no three-term increasing subsequence can be given by the Nth catalan number .. ?
More formally number of permutations such that there doesn't exist any i<j<k for which a[i]<a[j]<a[k].

someone please help me with this problem :
https://www.hackerrank.com/contests/projecteuler/challenges/euler050

https://www.hackerrank.com/contests/101hack41/challenges/the-forest-game

Can someone explain the idea behind this problem?
Editorial is not much clear,lacks proof.
Thanks.