You are tasked with writing a C$++$ program that allows the user to input a list of student ID numbers. Using the values in the list, perform the following functions:

a$.$ Sort the list using insertion sort. Implement the algorithm to achieve the best$-$case time complexity. The list should be sorted in ascending order.

b$.$ Search the sorted list for a specific student ID using sequential search. The time complexity of this search should be in the worst case.