Purple is Blind

A wise imposter turned off lights in a "codified among us game" to increase their chances of winning the game, Purple is near lights to fix it, she is assigned a task to complete in order to successfully turn on lights in the game. The task is as follows, given a sum $S$ and an array $A$ of size $N$, find whether it is possible to construct an integer AP [(Arithmetic progression)](https://www.c