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BORING - Boring Factorials (Reloaded) |
Factorial is one of the most attractive word this week, it is proposed to reload a famous problem. Is it so boring?
Sameer and Arpit want to overcome their fear of Maths and so they have been recently practicing Maths problems a lot. Aman, their friend has been helping them out. But as it goes, Sameer and Arpit have got bored of problems involving factorials. Reason being, the factorials are too easy to calculate in problems as they only require the residue modulo some prime and that is easy to calculate in linear time. So to make things interesting for them, Aman - The Mathemagician, gives them an interesting task. He gives them a prime number P and an integer N (not so) close to P, and asks them to find N! modulo P. He asks T such queries.
Input
The first line of input contains an integer T, the number of test cases.
On each of the next T lines, your are given two integers N, and P a prime number.
Output
For each test case, you have to print N! modulo P.
Example
Input: 3 2 5 5 11 21 71 Output: 2 10 6
Constraints
0 < T < 104
0 < N < 4×1018
1 < P < 4×1018, a prime number
Abs(N-P) < 104
Problem designed to be solvable using some 'slow' languages like Python (333B of code). It is highly recommended to solve in a very fast way the original problem! Basic solution, even in fast language should give TLE. Time limit is set as sqrt(correct × basic). The "basic" code gave me 0.00s to the original problem with slow IO. If you don't find this reload edition hard enough, please consider the challenge edition with more serious constraints. ;-) Have fun.
| Added by: | Francky |
| Date: | 2014-03-03 |
| Time limit: | 2.5s |
| Source limit: | 50000B |
| Memory limit: | 1536MB |
| Cluster: | Cube (Intel G860) |
| Languages: | All except: ASM64 |
| Resource: | DCEPC11B |
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2014-03-08 07:54:53 anurag garg
Francky sir I am getting WA but I got AC on DCEPC11B in 0.02 sec can you tell me where my code fails and is there any chance to get AC in time? submission id:11208025 thanks --ans(francky)--> You used a basic method, but a fast language ; it's possible but hard to get AC. You have overflow problems (you should try FIB64 for that, in Python and after in C/C++ ). It can be simpler to get AC here with a really different method. Good luck. --anurag-> thanks for the suggestion sir i will try to solve Last edit: 2014-03-08 09:08:24 |
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2014-03-04 19:21:54 [Lakshman]
@Francky is there any chance of AC with my approach? --ans(francky)--> Your approach seems too simple here to get AC in time. You should get 0.00s easily on the original problem before trying this one. Just an advice ;-) Lakshman-->PIKE really helped me. --ans(francky)--> Good job, stage 1 done. Now you can try new ideas ;-) with the challenge edition, or try to get AC at BORING2. Lakshman-->Right now I have no Idea how to approach BORING2 But I will keep trying. One thing I would say your problems are awesome. --ans(Francky)--> Thanks for your appreciation. Last edit: 2014-03-06 10:53:16 |
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2014-03-04 13:58:39 Francky
This reload edition wasn't hard enough, although not an easy one. Please consider the challenge edition with more serious constraints. Have fun ;-) Last edit: 2014-03-04 20:07:22 |
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