Let $\varphi:(A,\mathfrak{m})\to(B,\mathfrak{n})$ be a local morphism of regular local $\mathbb{C}$-algebras which makes $B$ integral over $A$. If $\mathfrak{m}=(x_1,\ldots,x_d)$ is a regular system of parameters of $A$, is it possible to choose a regular system of parameters $\mathfrak{n}=(y_1,\ldots,y_d)$ for $B$ such that $\varphi(x_i)=y_i^{n_i}$ for certain integers $n_i$? If not, can I add any conditions that will give me such a result?