Choir circle cuts

Find who is left standing when a choir director thins out a circle of singers with a deck of counting cards.

singers singers stand in a circle on the risers, numbered 1 to singers clockwise. The director keeps a deck of step cards cards, used over and over in order (cards[0], cards[1], ..., then cards[0] again after the last).

The thinning goes in rounds until one singer is left:

1. The starter of the first round is singer 1.
2. In a round the director turns the next card, with value s, and counts s singers clockwise, beginning with the starter as count 1. The singer reached by count s is cut and leaves the circle. (If s is larger than the number of singers left, the count simply keeps going around.)
3. The next round's starter is the singer immediately clockwise of the one just cut.

The singer who is never cut is the winner. The runner-up is the singer cut in the very last round (when two singers were left). If only one singer was there to begin with, there is no runner-up.

For example, with 5 singers and cards [2, 3]: round 1 counts 1, 2 and cuts singer 2; round 2 starts at singer 3 and counts 3, 4, 5, cutting singer 5; and so on.

Input: singers, an integer, and cards, a list of integers.

Output: [winner, runner_up], both singer numbers; the runner-up is 0 when singers is 1.