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

You are a librarian tasked with merging the book inventories from two branches of the library. Each

branch has its list of books sorted by their unique identification numbers in non$-$decreasing order. The

central library's inventory system $($represented by nums$1)$ has been prepared to accommodate books from

both branches, with extra spaces $($initially set to zero$)$ reserved for the books from the second branch.

Details:

$$ nums$1$ represents the list from the central library, which already includes books from the first

branch and has extra space for books from the second branch.

$$ nums$2$ represents the list of books from the second branch.

$$ m is the number of books currently listed from the first branch in the central library.

$$ n is the number of books listed from the second branch.

Your task is to merge these two lists in a way that maintains the sorted order, with all the books listed

together in nums$1.$

Example $1$:

Input:

$$ nums$1=[101,102,103,0,0,0]($Books from the first branch with extra spaces for the second

branch$)$

$$ m $=3(3$ books from the first branch$)$

$$ nums$2=[102,105,106]($Books from the second branch$)$

$$ n $=3(3$ books from the second branch$)$

Output: nums$1=[101,102,102,103,105,106]$

Explanation: The merged book list maintains the non$-$decreasing order of book IDs.

Example $2$:

Input:

$$ nums$1=[101],$ m $=1(1$ book from the first branch, no extra space needed$)$

$$ nums$2=[],$ n $=0($No books from the second branch$)$

Output: nums$1=[101]$

Explanation: Since there are no books from the second branch, the list remains unchanged.

Example $3$:

Input:

$$ nums$1=[0],$ m $=0($No books from the first branch, one space for the second branch$)$

$$ nums$2=[101],$ n $=1(1$ book from the second branch$)$

Output: nums$1=[101]$

Explanation: Since there are no books from the first branch, the result is simply the list of books

from the second branch.

$$ nums$1.$length $==$ m $+$ n $($The total length of nums$1$ is enough to hold all books from both

branches$)$

$$ nums$2.$length $==$ n $($The length of nums$2$ is equal to the number of books in the second branch$)$

$0<=$ m$,$ n $<=200($Each branch can have up to $200$ books$)$

$1<=$ m $+$ n $<=200($The total number of books from both branches combined will be at most $200)$

$-109<=$ nums$1[$i$],$ nums$2[$j$]<=109($The book IDs can be very large numbers, representing

unique identification numbers$)$

You must write an algorithm with O$($m $+$n$)$ runtime complexity. Space complexity should be O$(1).$