prime to $p$-part of defining parameters of a hypergeometric motive (awaiting review)

For a hypergeometric motive with defining parameters $[A, B]$ and a prime number $p$, we define the prime-to-$p$-part $[A^p, B^p]$ as follows.

For each $u=a_i$ or $b_j$ in $A=(a_1,\ldots, a_m)$ and $B=(b_1,\ldots, b_n)$ we write $u=p^s v$ where $p \nmid v$. We replace $u$ with $\phi(p^s)$ copies of $v$, to get $[A', B']$, and then remove equal numbers of any overlapping elements between the multisets $A'$ and $B'$ to get $A^p$ and $B^p$.