Write the folllwing program:

a) Ask the user to insert the following keys to build a B-tree (order = 5):

3,7,9,23,45,1,5,14,25,24,13,11,8,19,4,31,35,56

b) Display the tree to screen

c) Base on the Searching Algorithm provided below, search the number 31 in the above B-tree, and display the path traversed.

Searching Algorithm Let x be the input search key . Start the searching at the root If we encounter an internal node v, search (linear search or binary search) for x among the keys stored at v Ifx