This question is similar to the question link.
Let $A= \mathbb C [t^2,t^{-2}]$ and $B= \mathbb C [t,t^{-1}]$. Given $r\in \mathbb Z_+$ and $f\in B$ with the form $f=(t-a_1)(t-a_2)\cdots(t-a_k)$, where $a_i\in \mathbb C\setminus \{0\}$ with $a_i^k\ne a_j^k$ $(i\ne j)$ for $k=1,2$, let $I$ be the ideal of $B$ generated by $f^r$. Define the natural map $\phi: A \to B/I$ by $t^k\mapsto \overline{t^k}$ for all $k\in \mathbb 2Z$.
QUESTION: Is the map $\phi$ surjective?
Notice that the link above mentioned is the particular case with $r=1$.