Rewrite Chinese Remainder Theorem implementation

[NabilMx99]

Changes:

• Deleted the old implementation and wrote a new one from scratch.
• Added detailed comments and documentation to explain the algorithm and code structure.
• Improved input validation and user prompts.
• Ensured the program checks for pairwise coprime moduli before computing the solution.

Testing:

• Manually tested the program with several sets of congruence equations.
• Verified correct results for known CRT examples.

Time Complexity : O(k × log²(n)), where k is the number of equations and n is the product of all moduli.