Construct a decidable set $B$ such that $B \neq A_w$ for any $w \in \Sigma^\star$ I've been stuck on this problem for a while. Any hints would be appreciated!

Let $A \subseteq \Sigma^\star$ be decidable. Given $w \in \Sigma^\star$, define $$A_w = \{x \in \Sigma^\star\:|\: \langle x, w \rangle \in A\}.$$ 
Construct a decidable set $B$ such that $B \neq A_w$ for any $w \in \Sigma^\star$.
Here is a hint. Let $w\in B$ if $w\not\in A_w$ and let $w\not\in B$ if $w\in A_w$.