e$)$ Consider the decision problem version of Fridge Stacking:

Fridge Stacking: Assume we have $n$ food items, called $1,$dots,$n,$ each of which

has a nonnegative integer size, called $a_i.$ Is it possible to place all items $1,$dots,$n$

in $M$ fridges that all have the same capacity $k,$ i$.$e$.$ each fridge can only hold

items the sum of their size is less or equal $k?$ We can assume that $a_i,MkM$

otherwise the problem $is$ trivial.

All numbers $a_i,M$ and $k$ are represented $in$ binary format.

Explain why Fridge Stacking $isinNP.$ Any algorithm $to$ show this can $be$

sketched, but runtime information must $be$ discussed clearly.