Ones and Zeroes

Consider two binary sequences $a$ and $b$ of length $n$ each. Let us call these sequences compatible if a \text{ xor } b = a + b, where $\text{xor}$ is the element-wise "exclusive OR" operation.

Given an integer $n$ and a pair of binary sequences $p$ and $q$, find the pair of compatible binary sequences $a$ and $b$ which comes first after the pair $(p,q)$. Pair $(a,b)$ is said to be lexicographically less that $(c,d)$ if $a$ is lexicographically less than $c$, or $a$ and $c$ are equal and $b$ is lexicographically less than $d$. If there is no pair of compatible binary sequences lexicographically greater than $(p,q)$, output the lexicographically first compatible pair.