Do you pay a site's coast or Hidden Place cost when travelling to an unrevealed site?

Question

Accepted Answer

Supply is paid before the travel resolves, so a modifier of the unrevealed destination (such as the coast modifier) cannot lower your cost. Revealing the facedown site costs nothing extra, because its power was not in effect at that moment.

Oath: Chronicles of Empire & Exile

Do you pay a site's coast or Hidden Place cost when travelling to an unrevealed site?