$8.[4$ marks$]$ Recall the bijection between the positive rational numbers Q and the positive integers N $.$ Write a C program to output the rational number that gets mapped to n$.$ Remember, to skip over the fractions that are not in reduced form. For example, the first $11$ such rational numbers are:

$1/1,2/1,1/2,3/1,1/3,4/1,3/2,2/3,1/4,5/1,1/5$

Hand in: Your C code and output the n$-$th rational numbers for:

$($a$)$ n $=11($should be $1/5)$

$($b$)$ n $=999$

$($c$)$ n $=1234567$

$($d$)$ n $=87654321$

$($e$)$ n $=999999999($nine $9$s$,$ my implementation took about $3$ minutes$)$