Communicating the Card

(An implementation of the algorithm described in part 5 of the paper Using a Card Trick to Teach Discrete Mathematics by Shai Simonson and Tara S. Holm.)
(I first heard about this trick in December 2017 from hpmetsfan.)

Assistant Instructions

Have the magician leave the room, and ask audience for five distinct numbers between 1 and 100, inclusive.
Type these numbers below, comma separated. (e.g. 27, 87, 93, 23, 59)
Audience numbers:
[?, ?, ?, ?] ← (Once you hit "Compute!", four of the numbers should appear here.)
Read the four numbers to the magician in the order that they appear.

Magician Instructions

Enter assistant's numbers below, comma separated. (e.g. 59, 87, 27, 23)
Assistant's numbers:
??? ← (Once you hit "Compute!", one number should appear here.)
Reveal the secret number to the audience!