Cake Making

There are exactly $100$ colours in the world, numbered $1$ to $100$. Chef is making a $2$-layered cake, and all that is left is deciding the colours of the $2$ layers. Chef has decided that we can choose any of the colours $1, 2, \ldots, A$ for the first layer, and any of the colours $1, 2, \ldots, B$ for the second layer. However, there is an **extra constraint**. To encourage diversity, the