DCEPC11B - Boring Factorials


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 close to P, and asks them to find N! modulo P. He asks T such queries.

Input

First line contains an integer T, the number of queries asked.

Next T lines contains T queries of the form “N P”. (quotes for clarity)

Output

Output exactly T lines, containing N! modulo P.

Example

Input:
3
2 5
5 11
21 71

Output:
2
10
6
Constraints:

1 <= T <= 1000

1 < P <= 2*10^9

1 <= N <= 2*10^9

Abs(N-P) <= 1000

hide comments
bikrambiswas: 2021-01-11 16:23:52

This is a great problem of(wilson+fermit) theorem
Unfortunately my penis is small tho

Last edit: 2021-01-11 16:26:37
yzs: 2020-09-25 14:10:39

good ques
wilson n little fermat
my ans for test case 1999554444 1999555444: 502781432

Last edit: 2020-09-26 10:52:23
smso: 2020-09-25 10:46:09

more testcases:
10
780 653
54 601
210 659
780 659
776 617
678 617
1110 631
1182 631
219 617
551 607

output:
0
1
581
0
0
0
0
0
503
509

profesir: 2020-09-02 18:21:09

don't use code from cp-algorithm..
search for compute n!modulo p gfg..
all the best for AC

nadstratosfer: 2020-07-15 20:18:53

There's something strange about the judge used here, wasted half an hour yesterday because an assert on n < p wouldn't trigger a NZEC. Tried without looking up anyone else's theorem several times last few years, had to give up on that but still passed with logic more straightforward than what others seem to be doing.

saint_sharan: 2020-06-14 18:43:36

My code is giving TLE, although I used the same algorithm given at CP-Algo page, including the condition when (n>=p). What's the method to remove that TLE?

kabbo25: 2020-04-26 03:00:10

Willson thoerem+check when n is greater than p then n goes up to p-1
then modulo multiplicative inverse

sajalagrawal14: 2019-07-29 12:48:35

ac in five go . dont use recusive fast modulo , use iterative

abhimanyu_1998: 2019-07-04 11:51:15

ac in one go

ashu12_chi: 2019-05-24 14:27:30

@anirudnits 502781432 answer from my AC
In case of n!%p==0 answer is p not 0


Added by:dce coders
Date:2013-10-01
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:C CSHARP C++ 4.3.2 CPP C99 HASK JAVA PAS-GPC PAS-FPC PYTHON PYTHON3 PY_NBC
Resource:Own Problem