MEXtreme Divisibility

The *div-MEX* of an array is defined to be the smallest positive integer that doesn't divide *any* element of the array. For example, the *div-MEX* of $[4, 10, 1, 9, 21]$ is $6$, because every integer from $1$ to $5$ divides at least one element of the array, but $6$ doesn't divide any of them. You're given an array $A$ of length $N$, and an integer $M$. The elements of $A$ all lie between $1$