Mean Difference (Hard)

*This is the hard version of the problem. The only difference between this and the easy version is that here, you must find the answer for every prefix of the array.* For an array $B$ of length $M$, we define the following: - $\text{avg}(B)$ is the *average* of $B$, rounded down. Formally, $\displaystyle\text{avg}(B) = \left\lfloor\frac{B_1 + B_2 + \ldots + B_M}{M}\right\rfloor$ where $\lef