Let $n$ and $k$ be integers, $1\le k\le n$. Find an integer $b$ and a set $A$ of $n$ integers satisfying the following conditions: (i) No product of $k-1$ distinct elements of $A$ is divisible by $b$. (ii) Every product of $k$ distinct elements of $A$ is divisible by $b$. (iii) For all distinct $a,a'$ in $A$, $a$ does not divide $a'$.