Please don't copy$/$paste from ChatGPT or any other LLMs and please give me a code in C to solve the following problem

Imagine a library maintains an inventory list of books based on their unique identification numbers $($IDs$),$

sorted in ascending order. For some reason, such as a shift in cataloging practices or a database update,

this list has been rotated at an unknown pivot point. Your task is to find the position of a specific book's

ID in this rotated list.

Details:

$$ nums represents the rotated sorted list of book IDs.

$$ target is the ID of the book you are trying to find.

The goal is to determine the index of the target book ID in the rotated list. If the book ID is not present,

return $-1.$

Example $1$:

Input: nums $=[104,105,106,107,100,101,102],$ target $=100$

Output: $4$

Explanation: The list $[104,105,106,107,100,101,102]$ was originally $[100,101,102,104,105,106,$

$107]$ and got rotated. The book ID $100$ is found at index $4$ in the rotated list.

Example $2$:

Input: nums $=[104,105,106,107,100,101,102],$ target $=103$

Output: $-1$

Explanation: The book ID $103$ is not present in the list.

Example $3$:

Input: nums $=[101],$ target $=100$

Output: $-1$

Explanation: There is only one book ID in the list, and it does not match the target.

Constraints:

$$ The length of nums is between $1$ and $5000.$

$$ The book IDs are unique and within the range from $-10^4$ to $10^4.$

$$ The list is sorted in ascending order but may be rotated.

You must write an algorithm with O$($log n$)$ runtime complexity.

Hint:$-($Binary Search mid and low comparison$)$