The monkey and the coconuts

To break a coconut, monkeys usually climb to the roof of an $n$-storey building and drop coconuts from the top. One clever monkey, tired of constantly climbing to the roof, decided to find the lowest floor from which a dropped coconut will break. The monkey can climb to any floor from $1$ to $n$ (the roof is considered to be the $(n+1)$-th floor) and throw a coconut out the window. If the coconut does not break when dropped, the monkey can use it again for further experiments. The monkey has exactly $k$ coconuts prepared for the experiments. The monkey needs to determine the desired floor number, using no more than $k$ coconuts. Also, the monkey would like to find the floor with the minimum number of throws, since it can only carry one coconut at a time, and for each throw, it must go down to the ground for another coconut prepared for experiments or for a previously thrown but unbroken coconut.

Write a program to plan the experiments in a way that minimizes the number of throws in the worst case. The plan must consider that the required floor could be any floor from $1$ to $n$, or it may be that the coconut only breaks when dropped from the roof.