The three, and Adham (with Halzoom) were deep in the Unknown. They met Abbas, an old man who cares for Halzoom. Abbas was worried. Halzoom, a special goose, had a strange eating plan, and it was hard to keep track.

Halzoom also had $$$M$$$ "3NTAR" cats (numbered $$$1$$$ to $$$M$$$) that needed food from his supply.

Here's Halzoom's feeding rule:

From Day 1: Each cat eats $$$1$$$ gram of dry food.

From Day 2: The food for cat $$$j$$$ on day $$$i$$$ is : (food for cat $$$j$$$ on day $$$i-1$$$) + (total food that cats $$$1$$$ to $$$j-1$$$ ate on the current day $$$i$$$).

Abbas needs help! He's particularly worried about the final meal: how much food will cat number $$$M$$$ eat on day $$$N$$$?

He needs this specific value to make sure Halzoom's provisions are managed correctly. If not, Halzoom might get upset, and its magic could go wrong.