Wristband freebies

Tally how many freebies each festival wristband earns across a row of stalls.

A festival hands out wristbands numbered 1 to total. Along the midway are several stalls, one per entry of intervals. Every wristband visits every stall once. A stall with interval k gives a freebie to a visiting wristband whose number is a multiple of k, so a wristband earns one freebie from each stall whose interval divides its number. Two stalls may have the same interval; they are still two separate stalls, each giving its own freebie.

Sort the wristbands by how many freebies they earned in total.

Input: total, the number of wristbands; intervals, the list of stall intervals.

Output: a list [none, odd, even] where none is the number of wristbands that earned no freebie, odd is the number that earned an odd number of freebies, and even is the number that earned an even number of freebies that is at least 2. The three values always add up to total.

total can be as large as a trillion, so handing out wristbands one at a time will not finish in time.