Is it possible to solve 3SUM in $O(n^2)$ time?

Problem: 3SUM

Input: Three lists A, B and C of integers and an integer k. Each list contain $n$ numbers.
Task: Decide whether there exists a tuple (a, b, c) ∈ A × B × C such that a + b + c = k.

Question : Is it possible to solve 3SUM in $O(n^2)$ time using constant space ? Prove or disprove it

A $O(n^2)$ algorithm (with $O(1)$ space) is as follows:

• Sort $A$, $B$, and $C$ individually in $O(n \log n)$.

• For each $a \in A$:

• Search a pair of $b \in B$ and $c \in C$ such that $b + c = k - a$. This can be done in $O(n)$ by traversing $B$ from the smallest to the largest and $C$ from the largest to the smallest. (Tip: Comparing $b + c$ with $k-a$ each time.)

StackExchange Computer Science Q#85715, answer score: 5