Ismail–Kim–Stanton's generalized Borwein sign conjecture

Let $a$ and $K$ be relatively prime positive integers with $1\le a\le K/2$ and $K$ odd. Define coefficients $b_m$ by

$$\prod_{i=0}^{n-1}(1-q^{a+iK})(1-q^{K-a+iK})=\sum_{m\ge0}b_mq^m.$$

Ismail–Kim–Stanton conjecture. If $m\equiv \pm(2l+1)a\pmod K$ for some $l$ with $0\le l<K/2$, then $b_m\le0$; otherwise $b_m\ge0$. Thus the sign of $b_m$ is determined by $m$ modulo $K$. The source attributes this generalization to Ismail, Kim, and Stanton and does not report a proof here.