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BORING - Boring Factorials (Reloaded)

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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.

Submit solution!

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	teequila_: 2021-01-31 20:11:26 Also here, runs very fast in my local testcases, but exceeds time limit for the submission. Any tips? Is the usage of BigInteger in java too inefficient for this problem? =(Francky)=> This problem is obviously intended to be solved without bigint library, any of them (even the best ones) will fail. It is an arithmetic modular problem. Regards, Last edit: 2021-02-08 17:05:07
	fanxin: 2021-01-29 16:14:38 @Francky Can you tell me why the result is "runtime error (NZEC)". I've tried different input, they can all give right answers. =(Francky)=> Try much more inputs via another I/O files created by bruteforce easy solution. Last edit: 2021-02-08 17:06:43
	jacobian_det: 2020-05-13 19:33:31 @Francky: How to avoid overflow issue giving WA in CPP? =(Francky)=> If you know how to do fast modular exponentiation, then you can apply method for modular multiplication, just replace (exp, mul) by (mul, add) in the method. Then you have no overflow issue. Good luck. Last edit: 2020-05-15 08:54:47
	Avik Sarkar: 2018-06-03 15:13:05 HI. I used Willson's theorem + Inverse Modulo . Can anyone suggest me a hint of any faster way. Here is my submission: ************ edited ***** ( Please edit if it violates rules. But please give a hint. ) =(Francky)=> No hint here ; except : try to solve various problems to find some hints. =>(Avik Sarkar) => I solved the first and easy one using the way I mentioned above. But solving in the same way I got TLE. Can you just tell me am I in a correct way or not ? Last edit: 2018-06-03 18:28:14**
	free mind ;): 2015-09-26 09:16:29 @Francky sir can you tell why i am getting runtime error , i am new in python, is this because range function or something else and can you please tell why my c++ solution giving WA . :)
	vishu: 2015-08-13 03:00:17 @Francky sir,can you please tell me for what test cases it is giving wrong answer.Is it a specific input or it is giving wrong answer due to overflow? submission id-14880828 =(Francky)=> You have WA for almost all input ; good luck. Finally Ac! learnt python to do this Last edit: 2015-08-29 23:01:24
	Curiosa: 2015-03-18 18:13:33 @Francky, could you please check my solution? Is the idea behind my solution "basic" (in your terms)? My solution is still slow compared to others, is this because of Java? (Francky) => Java could be faster than Python for that task, and your method could give TLE with Python. It is a basic one, using java (or Python) it is easy to implement some nice improvements. Good luck. @Francky, I have developed some of my ideas, can I further develop my idea or do I need to come up with something completely different to achieve lower time limit? can you give me any hints? Last edit: 2015-03-25 13:58:16
	ivar.raknahs: 2014-11-04 16:14:49 @francky=> can u tell me where my code fails (id:12812179) and can i get AC with this kind of approach?. Thanks --ans(Francky)--> You have a slow but correct python code, you'll can easily find some troubles in your C++ code, like negative outputs and most of WA cases. Good luck. Last edit: 2014-11-04 20:54:35
	Tarun Garg: 2014-07-27 19:03:12 @Francky where my code is falling out..? is there any chances to get Ac..? --ans(Francky)--> Not with this kind of code. Sorry... You should try some brute force with Python, and find some new ideas to get AC in time. Last edit: 2014-07-27 21:12:20
	[Lakshman]: 2014-03-09 15:09:59 @Francky Finally Accepted with C++ but with worst running time. --ans(francky)--> I see that, but those experiments will give solutions to get AC in Extended or more points in Challenge ; you're doing right things. Lakshman--> Thanks I will do that. Last edit: 2014-03-09 15:37:26

Submit solution!

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