Goal
You have to decompose a positive integer/fraction as a product of powers of factorials of prime numbers.
For example,
22 = (11!)^1 × (7!)^(−1) × (5!)^(−1) × (3!)^(−1) × (2!)^1
10/9 = (5!)^1 × (3!)^(−3) × (2!)^1
Use this special notation: prime number#power
to denote each term, e.g. (11!)^4 is denoted as 11#4.
Output the non-zero terms only, with space separation, and order them in descending order of the prime numbers.
The above examples hence become:
22 = 11#1 7#-1 5#-1 3#-1 2#1
10/9 = 5#1 3#-3 2#1
Input
Line 1: a positive number N, that can be either an integer or a fraction of the form numerator/denominator.
Output
Line 1: The ordered list of the non-zero terms of the decomposition of N, denoted using the special notation.
Constraints
0 < N, numerator, denominator < 20000
Every prime involved is less than 2000.
