SOLVE
LATER
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:
$$1 \le T \le 10^5$$
$$1 \le N \le 10^{18}$$
Challenge Name
Sapient Global Markets Core Java Hiring Challenge
Sapient Global Markets Core Java Hiring Challenge