Write a method called insertAt that takes an index, an integer n, and a value as parameters, and that inserts n copies of the given value at the given index in a list of integers. For example, if a variable called list stores this sequence:

 [12, 42, 8, 934] 

and the following call is made:

 list.insertAt(2, 4, 98); 

then it should store the following values after the call:

 [12, 42, 98, 98, 98, 98, 8, 934] 

Notice that there are now four occurrences of the value 98 starting at index 2 and that later values are in the same order as in the original.

You are writing a method for the ArrayIntList class discussed in lecture:

 public class ArrayIntList { private int[] elementData; // list of integers private int size; // current # of elements in the list } 

Your method should throw an IllegalArgumentException if the index is less than 0 or greater than the number of elements in the list or if the value of n is less than 0. You are not to call any other ArrayIntList methods to solve this problem, you are not allowed to define any auxiliary data structures (no array, ArrayList, etc), and your solution must run in O(n) time where n is the length of the list. You may assume that the array has sufficient capacity to store the new values.