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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

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)

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