Suppose $x$ is an $N=2^n$ elements database. Let's define a $2N$-bit database with $y \in \{0,1\}^{2N}$ indexed by $(n+1)$-bit strings $j=j_1\ldots j_n j_{n+1}$, where \begin{align} y_j=\begin{cases}1 & \text{if }x_{j_1 \ldots j_n}=1 \text{ and } j_{n+1}=0 \\ 0 & \text{otherwise} \end{cases} \end{align}
How can one implement the oracle $|j \rangle \rightarrow (-1)^{y_j} |j\rangle$ using one query to the $x$ oracle $O_x: |i,b \rangle \rightarrow |i, b\oplus x_i \rangle $ and some elementary gates?
Edit: Basically what would do the job on a high level would be to check if the the result of $O_x$ was 1 or 0. If it was 1 a controlled gate on $j_{n+1}$ that flips everything again if $j_{n+1}$ is 1 and do nothing otherwise, if it was 0 do nothing. At least this is my intuition but I cannot formalize it.