There are $n$ horses. At a time only $k$ horses can run in the single race. How many minimum races are required to find the top $m$ fastest horses? Please explain your answer. (There is no timer.)


This was asked and not (yet) answered at [math.stackexchange](https://math.stackexchange.com/questions/209790/how-to-find-a-total-order-with-constrained-comparisons). 

The $n = 25, k = m = 5$ case was a Google interview question and there are various answers on the web. But I am not sure what should be the right answer for this. Any ideas?