Leave no Witnesses

Let $B$ be a **binary** string of length $N$. The integer $X$ is said to be a *witness* for $B$ if the following condition holds: - Consider two arrays $S_1$ and $S_2$, initially both empty. - For each index $i$ ($1 \leq i \leq N$), - If $B_i = 0$, append $(X \ \& \ i)$ to $S_1$. Here, $\&$ represents the bitwise AND operation. - If $B_i = 1$, append $(X \mid i)$ to $S_2$. Here, $\mi