A problem about checking isomorphism of R-module

Question

Let $R=K\left[x_1,x_2,\cdots,x_n\right]$ be a polynomial ring with coefficients in the field $K$; $\alpha_1,\alpha_2,\cdots,\alpha_p,\beta_1,\beta_2,\cdots,\beta_q\in R^{1\times m}$; $M_1$ be the $R$-module generated by $\alpha_1,\alpha_2,\cdots,\alpha_p$; and $M_2$ be the $R$-module generated by $\beta_1,\beta_2,\cdots,\beta_q$. How to check if $R^{1\times m}/M_1\cong R^{1\times m}/M_2$ is true or not?