Golf a FRACTRAN interpreter
From the Esolangs wiki,
- a program consists of a finite list of positive, rational numbers.
- The input to a program is a positive integer n.
- The list is then searched in order, for a rational number $p/q$ such that $n×p/q$ is an integer.
- Then n is replaced by $n×p/q$ and the search is restarted from the beginning of the list.
- The program halts when no such number $p/q$ can be found, and the final n becomes the output from the program.
- Output the final value of $n$.
Your task is to implement an interpreter for this language.
You are to take two inputs:
- $n$, an integer
- $A$, an array of fractions, which may be taken as a list of pairs, or in the rational datatype of your language.
A single integer, the final value of $n$.
program input output
78/55, 5/3, 1/5, 11/2, 5/7 1096135733 328842888196762472689573703 3/2 1296 6561 455/33, 11/13, 1/11, 3/7, 11/2, 1/3 72 15625