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Euler's Exponents
Tag(s):

Medium, Modular exponentiation

Problem
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Given four numbers A , B , C and P where P is prime number .

( A B C ) % P = ( A ( B C ) % phi(P) ) % P

where \(phi(P)\) is the Euler's Totient Function of P .

However the equation is restricted only to the prime numbers.

Write a program to solve this problem if the given P is not \(Prime\) .

Input Format
First line of input contains a single integer T denoting the number of test cases. First and the only line of each test case contains four space separated A , B , C and P.

Output Format
For each test case , Print the required answer .

Input Constraint
\(1 ≤ T ≤ 10\)
\(1 ≤ A ≤ 10^9\)
\(1 ≤ B ≤ 10^9\)
\(1 ≤ C ≤ 10^5\)
\(1 ≤ P ≤ 10\)\(18\)

SAMPLE INPUT
2
3 3 3 777
3 5 2 10
SAMPLE OUTPUT
258
3

Explanation

Test 1 : A = 3 B = 3 C = 3 P = 777 (A^(B^C)) %P = 258 Test 2 : A = 3 B = 5 C = 2 P = 10 (A^(B^C)) %P = 3

Time Limit: 1.0 sec(s) for each input file.
Memory Limit: 256 MB
Source Limit: 1024 KB
Marking Scheme: Marks are awarded when all the testcases pass.
Allowed Languages: C, C++, C++14, Clojure, C#, D, Erlang, F#, Go, Groovy, Haskell, Java, Java 8, JavaScript(Rhino), JavaScript(Node.js), Julia, Kotlin, Lisp, Lisp (SBCL), Lua, Objective-C, OCaml, Octave, Pascal, Perl, PHP, Python, Python 3, R(RScript), Racket, Ruby, Rust, Scala, Swift, Swift-4.1, Visual Basic

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HackerEarth

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