Let $(A,m,k)$ be a local ring, and $A$ is a finitely generated $k$-algebra, and the maximal ideal $m$ is nilpotent. Let $x_1,\ldots,x_n \in m$ and their canonical images in $m/m^2$ generate this $k$-vector space.
How to show that $x_1,\ldots,x_n$ generate $A$ as $k$-algebra?