[Haskell-beginners] Finding the lowest element greater or equal than

Hello all, I want to find the lowest element in a collection of items which is greatet or equal to a given element. There can be more than one such element in which case I wouldn't care which one I get. I still want to be able to iterate over the elements following the found element. In a way I want the equivalent of select ... from table where table.x > n How would I do this efficiently? I tried using an ordered list, but I would still have to traverse half the list on average. I suppose I can do this with some sort of tree, but i don't want to write all the code myself. But I couldn't find anything off the shelf.