A question on algebraically closed field

Question

Let $k$ be an algebraically closed field . Consider the commutative ring , with unity , $A=k^\mathbb N=\prod_{i\in \mathbb N}k$ . Consider the proper ideal $I=\oplus_{i\in \mathbb N}k(=k^{(\mathbb N)})$ of $A$ ; let $m$ be a maximal ideal of $A$ containing $I$ . Then $A/m$ is a field . Is it true that $A/m$ is algebraically closed and is uncountable ?