Cut Wood / Facebook Interview
Overall I think you have about the simplest you could hope for. The only thing I'd do is set your bounds better. You know that you can do min(array)/ceil(k/len(array)) and you know you at most you can do max(array)/floor(k/len(array)).

I was going to suggest going for extra credit with a more sophisticated algorithm, but I don't think you can beat what the binary search approach. At worst you're going to be 32 or 64 * O(n). Given the simplicity of the algorithm I think that will likely beat sorting and all the alternatives I can think of either explicitly or implicitly do a sort which would be O(n log n).