If we want to construct a PRF that is length preserving, it is easy to show with hybrid proof that the resulting construction is a PRF.
But what happens when we have longer input. Supose that the key and output length are $n$ and the input size is $2n$.
I have been imagining what could happen to the binary tree. I feel like since input is double the size it will go double the depth. But in this case I cant tell if the resulting construction is a PRF.
Any hint would be helpful!