Through all the South of Brazil it is possible to find many species of spiders belonging to the genus Loxosceles, popularly known as recluse spiders, or brown spiders. Despite not being aggressive, these spiders inoculate a strong venom, being responsible for the greatest amount of accidents with spiders in Brazil. Accidents with recluse spiders usually occur when they hide inside shoes and clothes or under bed linen.

Some people mistake recluse spiders for spiders of the genus Nesticodes, popularly known as red house spiders, also very common in the South of Brazil. Harmless to humans, red house spiders are natural predators of recluse spiders and should not be eliminated.

To the left, a recluse spider. To the right, a red house spider.

Arthur and Merlin decided to play a dangerous game with spiders, which you shouldn't try at home. Arthur begins collecting N ≥ 1 spiders of the genus Nesticodes and N spiders of the genus Loxosceles, arranging the 2 × N spiders in a circle in a manner that the harmless spiders occupy the first N positions and the recluse spiders occupy the last N positions. Then, Merlin tells a positive integer K to Arthur, who enters a process of killing every K-th still living spider in the circle until exactly N spiders have been killed. Merlin's goal is that only recluse spiders are killed. For example, if N = 3 and K = 5, the spiders in positions 5, 4, 6 are eliminated, in this order, and Merlin reaches his goal, winning the game. If N = 2 and K = 7, the spiders in positions 3, 4 are eliminated, in this order, and Merlin also wins the game. However, if N = 3 and K = 10, the spiders in positions 4, 3, 6 are eliminated, in this order, and thus Arthur wins the game.