Please give me the correct answer.Problem $2(20\%)$ Consider the problem of using an array to store a sequence of items. Initially, we

have an empty array of size $1.$ When an element arrives, we insert it into the next empty slot, if it is

available. If no more slots are available in the current array, we create a new array with double size,

transfer all elements from the old array to the new array, and discard the old array. We will need to

create a new array upon inserting items numbered $2,3,5,9,17,$ etc. Suppose that inserting an element

to an empty slot and transfering an element both have cost $1.$ Prove that the amortized cost of inserting

items is O$(1).$