You have a stack of \(n\) pancakes of varying sizes on a griddle. Your goal is to rearrange the stack in order so that the largest pancake is on the bottom and the smallest one is on top. You are only permitted to flip the top \(k\) pancakes, thereby reversing their order. Devise a recursive scheme to arrange the pancakes in the proper order that uses at most \(2 n-3\) flips.