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I hope you will join your fellow programmers and enjoy the contest problems. Joining me on the problem setting panel are:

- Tester: DarkestLight (Mohammad Nematollahi)
- Editorialist: Deadwing (Hussain Kara Fallah)
- Statement Verifier: Xellos (Jakub Safin)
- Setters: kingofnumbers (Hasan Jaddouh), deva2802 (Devanshu Agarwal), pi-nan (Shivam Gor), Abhinav Jain
- Mandarin Translator: huzecong (Hu Zecong)
- Vietnamese Translator: Team VNOI
- Russian Translator: Fedosik (Fedor Korobeinikov)
- Bengali Translator: solaimanope (Mohammad Solaiman)
Hindi Translator: Akash Shrivastava

#### Contest Details:

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Auto comment: topic has been updated by deva2802 (previous revision, new revision, compare).How do you solve EVILAND?

How to solve Evil Land?

My solution: find the periodicity of F (i.e. ) then get the LCM of the periodicity of each

A_{i}. Finally, remove elements from A which have (in their periodicity) a prime with power larger than the power of the same prime in the periodicity of F (try for each prime in F).This gave TLE because I find the periodicity in for each number.

Why does taking the LCM help? I'm not able to understand what's going on.

If a number

Xhas a periodicityPon a moduloMthenX^{i}will equal all numbersYsuch thatYhas a periodicityQwhereQis a divisor ofP. If two numbersaandbhave a periodicityP_{a}andP_{b}then has a periodicity ofLCM(P_{a},P_{b}).So the problem is now to remove some elements of

Asuch that the LCM of their periodicity of the remaining is not a multiple of the periodicity ofF.To prove that, let

Xbe a number which has a periodicityPandX^{i}equalsYwhich has a periodicity ofQ. Then . Then , which means thatQis a divisor ofP. Remember that bothPandQare divisors ofM- 1 becauseX^{φ(M)}= 1.When will the problems be available for practice?

EVILAND: g(x, MOD) = periodicity of x in mod MOD. Make a[i] = g(a[i], MOD) and now the problem is removing some elements so that the lcm of the remaining elements isn't a multiple of g(F, MOD). Didn't submit because I started the contest in the last hour but I'm pretty sure this is correct. To prove this, transform multiplication to addition with a primitive root and the problem is the same but with addition.

How to solve TWOARR without persistent implicit treap or lazy updates with persistent seg tree? I solved it using lazy update with persistent seg tree but my constant was complete shit and it barely passed the TL with log^2 updates/queries.

I did the same in EVILAND but got TLE.

For TWOARR: sqrt-decomposition passed in ~2seconds

You can preprocess the primes and find periodicity in log^2 like this

It solves each case in O(N*log^2).

Setter code for TWOARR was n*log^2 . It passes in 1.8sec.

There exist sqrt deco solutions too.

How would you handle the queries using sqrt decomposition? especially the query of the first type.

Decompose array A, into root(n) blocks, then every query of type two can be handled in O(root(n)logn), using a flag to rebuild a block. For this we need to maintain a persistent seg tree on B. adjusting the Block size gives O(nroot(nlogn)) solution.

Yeah. Thought the same. just idea of persistent to handle the update of the value of b slipped out of my mind. Thanks.

what is persistent st?

Thanks for the problem, got my lazy ass to finally code persistent random BST. https://www.codechef.com/viewsolution/23140693 O(N * logN) expected time solution.

hey u coded treap . whats the difference between persistance tree and treap are both same

They aren't. Persistent treap doesn't really work because expected height breaks when you merge a treap with itself (due to how priorities work in treaps) but you can use a different randomization during merge (that I really can't explain why it works other than it makes every node have the same probability of being the root in a subtree). This different randomization is leftSide function in my code, I think you can't call this a treap anymore since it doesn't have heap properties.

ok

For EVILAND I found primitive root and all its degrees, and sorted that information, that allows to find the discrete log for each number in

O(1), givingMlogM+Noverall, which passed for mewhat is primitive root. and what is discrete log

I don't know, I just googled it!

ok

Almost a week since the contest and I still can't find the EVILAND editorial.