All Tracks Math Problem

Micro and Optimus Prime
Tag(s):

Easy, Math

Problem
Editorial
Analytics

Micro has discovered new type of numbers, he is calling them Optimus Primes. He defined a function,$$$f(x) = sum \space \space of \space powers \space of \space prime \space factors \space in \space x's \space prime \space factorization$$$ A number $$x$$ is Optimus Prime if $$f(x)$$ is exactly $$1$$ less than its total number of divisors. Now, Micro is interested in finding out the smallest Optimus Prime having $$f(x) = N$$. Help Micro with this task.

Input:
First line consists of a single integer $$T$$ denoting the number of test cases.
Each of the following $$T$$ lines consists of a single integer denoting $$N$$.

Output:
Print the required answer for each test case in a new line. Since answer can be large print it modulo $$10^9+7$$.

Constraints:
$$1 \le T \le 10^5$$
$$1 \le N \le 10^{18}$$

SAMPLE INPUT
1
2
SAMPLE OUTPUT
4
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++, Clojure, C#, D, Erlang, F#, Go, Groovy, Haskell, Java, Java 8, JavaScript(Rhino), JavaScript(Node.js), Lisp, Lisp (SBCL), Lua, Objective-C, OCaml, Octave, Pascal, Perl, PHP, Python, Python 3, R(RScript), Racket, Ruby, Rust, Scala, Scala 2.11.8, Swift, Visual Basic

CODE EDITOR

Initializing Code Editor...
Your Rating:

Contributor

This Problem was Asked in

Sapient Global Markets

Challenge Name

Sapient Global Markets Core Java Hiring Challenge

OTHER PROBLEMS OF THIS CHALLENGE
Notifications
View All Notifications