The owner of target nonland permanent puts it on their choice of the top or bottom of their library.
That permanent's controller chooses whether to put it on the top or bottom of the library. If the target permanent is made up of multiple cards (due to mutate or meld, for example), that permanent's controller puts all of them on the top or all of them on the bottom. They do not need to reveal the order those cards were put into the library this way.
