# AGS – Aritho-geometric Series (AGS) Solution

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## AGS Statement

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

Arithmatic progression(AP) is a set in which the difference between 2 numbers in constant. for eg, 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 same. for eg, 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 eg .. lets say d=1 and r=2 and a(1) = 1..

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’  &  ‘r’ to find the a(n) term .

sicne the numbers can be very large , you are required to print the numbers modulo ‘mod’ – mod will be supplied int 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

firts line will have 3 numbers ‘a’ ,’d’  and   ‘r’

2nd line will have 2 numbers ‘n’ & ‘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.

## AGS Solution

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