Hello again, It’s Arpa as usual :P. Hope you enjoyed from the Gym, and it’s here is the editorial.

Preparation details:

The problems authored by me when the main contest was authoring. Here is a table, showing percentage of expected accepts (in my opinion, before the contest) and the number of accepts.

Difference from main problems

A : n is bigger, binary_pow will not work. You need to calculate in a faster way.

B : n and also numbers are much bigger, simple xor will not work.

C : n is bigger, simple LCM will not work because answer would become really large.

D : Number of alphabet’s are 26 instead of 22, so it isn’t possible to allocate a array with size 2^z (z = 26).

Hints

A : Write last digit of 1378ⁿ for several small values. Calculate in a fast way.

B : Note that if then . Use trie.

C : If the answer exists, it depends on the lengths of cycles in the functional graph. Factorize numbers and calculate LCM.

D : Keep a mask for each vertex, i-th bit of mask_v is true if the number of edges in the path from root to v such that letter i is written on them is odd. Now if number of bits in is 0 or 1, path between v and u is Dokhtar-kosh. Give id to each mask.

Details

First accepts: A : retired_coder, C : wrinx.

Funniest code : shengdebao ’s code : 23229169. He was managing to get accepted in problem C, with a solution :O.

Solutions

I’d like to finish the editorial with below poem by Saadi Shirazi:

Translation: No one knows value of good friend as I know, fish will know the value of water when it fall on the beach.

Goodbye ; )