AGS - Aritho-geometric Series (AGS)

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Arithmetic and geometric progressions are 2 of the well known progressions in maths.

Arithmetic progression (AP) is a set in which the difference between 2 consecutive numbers is constant. For example: 1, 3, 5, 7, 9... In this series the difference between 2 numbers is 2.

Geometric progression (GP) is a set in which the ratio of 2 consecutive numbers is the same. For example: 1, 2, 4, 8, 16... In this the ratio of the numbers is 2.

What if there is a series in which we multiply a(n) by 'r' to get a(n+1) and then add 'd' to a(n+1) to get a(n+2)?

For example: let's say d = 1 and r = 2 and a(1) = 1, the series would be 1, 2, 4, 5, 10, 11, 22, 23, 46, 47, 94, 95, 190...

We add d to a(1) and then multiply a(2) with r and so on.

Your task is, given 'a', 'd' and 'r' to find the a(n) term.

since the numbers can be very large, you are required to print the numbers modulo 'mod' - mod will be supplied in the test case.

Input

First line of input will have number 't' indicating the number of test cases.

Each of the test cases will have 2 lines. The first line will have 3 numbers 'a', 'd' and 'r'. The second line will have 2 numbers 'n' and 'mod'.

a = first term of the AGS.

d = the difference element.

r = the ratio element.

n = nth term required to be found.

mod = need to print the result modulo mod

Output

For each test case print "a(n) % mod" in a separate line.

Example

Input:
2
1 1 2
13 7
2 2 2
10 8

Output:
1
6

Explanation

For the first test case the series is 1, 2, 4, 5, 10, 11, 22, 23, 46, 47, 94, 95, 190..., the 13th term is 190, and 190 % 7 = 1.

Notes

The value of a, d, r, n and mod will be less than 108 and more than 0.

For every series, the second term will be a+d and third term will be (a+d)*r, and so on.


hide comments
David: 2021-10-27 05:43:51

Great problem. Solved after 6 months.

Rajat Singh: 2015-08-18 11:30:34

excellent one!!!!!learned a very unique concept!!!!!!!!!!

Babu: 2015-07-30 18:01:26

where are the fucking constraints??? -_-

Bhuvnesh Jain: 2015-07-19 09:40:56

What a brilliant question! Finally ac after long struggle. New method for sum of GP.... Can't believe it was AC in 0.00 sec.... phew

ABHISHEK004: 2015-02-26 22:57:27

tried after 2 years ...
finally accepted :)
feeling relaxed

i need you: 2014-12-29 21:09:06

very nice problem...wasted 2 days
but finally got AC.

Aditya Paliwal: 2014-12-17 23:10:11

Took just 5 mins to derive formula but 4 hours to code it! Amazing problem! Seemed like I have solved similar problems before but I had to learn something new :) Awesome!

Last edit: 2014-12-17 23:10:38
Prateek chandan: 2014-08-25 23:49:28

I have tried for all test cases but still WA
Please help
ID : 12235014

Smriti Vashisth: 2014-05-22 16:03:32

getting WA despite checking all the cases
plz help Devil D
<snip>

Last edit: 2022-07-14 22:05:23
Piyush Raman Srivastava: 2014-01-22 13:28:32

wrong assumptions by problem solvers and an awesome mathematics!! Thanx a lot @Devil D :)


Added by:Devil D
Date:2012-03-09
Time limit:1s
Source limit:10000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:Own