$[$Q$2]$

Suppose that we have a stack $S$ that supports the following operations: Push $(S,x),$ which pushes an element

on top of the stack S$,$ Pop $($S$),$ which removes the element at the top of stack S$,$ and MultiPop $($S$,$k$),$ which

removes the top $k$ elements from the stack $S($if we try to remove more elements than the current number of

elements on the stack in a Pop or MultiPop operation, only the elements currently on the stack will be

returned$).$ Assume that the stack is initially empty. Give a potential function argument showing that the

amortized running time of each of the three stack operations is $(1).$