Suppose that a charged particle is held at the center of two concentric conducting spherical shells $A$ and $B,$ as shown in the above figure. The radius of sphere $A$ is $r_A=2\text{ cm}$ and that of sphere $B$ is $r_B=4\text{ cm}.$ The net flux $\Phi$ through a Gaussian sphere centered on the particle is $\begin{aligned} -16.0 \times 10^5 \text{ N}\cdot\text{m}^2\text{/C} &\text{for } 0 < r < r_A \\ +8.0 \times 10^5 \text{ N}\cdot\text{m}^2\text{/C} &\text{for } r_A < r < r_B\\ -4.0 \times 10^5 \text{ N}\cdot\text{m}^2\text{/C} &\text{for } r > r_A, \end{aligned}$ where $r$ is the radius of the Gaussian sphere. Then what are the net charges of shell $A$ and shell $B,$ respectively?

The value of the permittivity constant is $\varepsilon_0=8.85 \times 10^{-12} \text{ C}^2\text{/N}\cdot\text{m}^2.$