There are k ants on 1-meter stick. Each ant takes 1 second to walk the length of the stick. At time t = 0 seconds, each ant chooses a direction (left or right) and walks in that direction until it either falls off the stick or bumps into another ant. If it bumps into an ant, both switch directions. In terms of k, what is the max. time it will take for all the ants to fall off? What about the min. time?

Please solve clearly.