# Minimum pumping length of concatenation of two languages

there’s this small part of my homework that I just can’t figure out.

Let us denote $$p(L)$$ as the minimum pumping length of some language $$L$$. I’m supposed to find two regular languages $$A,B$$ so that

$$p(AB)=p(A)+p(B)$$

But whatever I try, I can only find languages so that

$$p(AB) < p(A)+p(B)$$

I’ve been sitting at this the whole day and I’m just going in circles. Can someone please give me a hint?