$2)$ Modern processors support different page sizes such as $4$KB and $2$MB$.$ Let's assume that you are tasked with designing two page tables supporting both regular pages $(4$KB$)$ and hugepages $(2$MB$).$ The virtual address size is $48$ bits and the physical address space size is $34$ bits. What is the total size of the page tables if the first table uses write$-$back and the second table uses write$-$through methods?

Please show your work for partial credit.$($Only providing an answer will not get full credit$)(25$pt$)$