Hot Potato

Hot Potato

There are N people seated at a round table. A hot potato is placed on the table.
The potato is passed clockwise around the table to M-1 people. The Mth person
to receive the potato leaves the table. The potato is then passed again.
This procedure is repeated until the table is empty.  The last person to leave
is the winner.

Diagram of the Hot Potato solution when N = 9 and M = 5

1 2 3 4 5 6 7 8 9      remove 5

1 2 3 4   6 7 8 9      remove 1

  2 3 4   6 7 8 9      remove 7

  2 3 4   6   8 9      remove 4

  2 3     6   8 9      remove 3

  2       6   8 9      remove 6

  2           8 9      remove 9

  2           8        remove 2

              8        winner

Write a computer program to simulate the hot potato game.  Given values
for N and M as inputs, it should produce a display like the one above.