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Ross and UNAGI
Tag(s):

Easy-Medium

Problem
Editorial
Analytics

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Rachel and Phoebe are sick of Ross trying to teach them the importance of UNAGI and decide to give him a problem to keep him busy . Ross asks for your help to solve the problem :

You are given Q queries containing two integers a,b . Your task is simple. Calculate sum of prime factors of
(\( a^{b^{c}} \) + 1)%m where m is \( 10^{6} + 3 \)

Input :

First line contains single integer Q .
Next Q lines contain three spaced integers a,b,c.

Output :

For each query output the answer in a new line.

Constraints :

\( 1 \leq Q \leq 10^{6} \)

\( 0 \leq a,b \leq 10^{9} \)

\( 0 \leq c \leq 10^{18} \)

Problem Setter - Vaibhav Bansal

SAMPLE INPUT
2
2 3 2
3 2 2
SAMPLE OUTPUT
28
43
Time Limit: 3.0 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: Bash, C, C++, C++14, Clojure, C#, D, Erlang, F#, Go, Groovy, Haskell, Java, Java 8, JavaScript(Rhino), JavaScript(Node.js), TypeScript, 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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