The Josephus problem is the

following game: $N$ people, numbered

$1$ to $N,$ are sitting in a circle. Starting

at person $1,$ a hot potato is passed.

After $M$ passes, the person holding

the potato is eliminated, the circle

closes ranks, and the game continues

with the person who was sitting after

the eliminated person picking up the

hot potato. The last remaining person

wins. Thus if $M=0$ and $N=5,$ players

are eliminated in order and player $5$

wins. If $M=1$ and $N=5,$ the order of

elimination is $2,4,1,5.$

a$.$ Write a pseudocode to solve

the Josephus problem for

general $($integer$)$ values of $M$

and N$.$ Try to make your

program as efficient as

possible. Make sure you

dispose of cells.

b$.$ What is the running time of

your program?