Assume that this program is run on a processor with a data cache of $4096$ bytes. Each block of the cache is $128$ bytes. Memory addresses are of $32$ bits. Data in arr$1$ and arr$2$ are stored in contiguous memory locations, i$.$e$.,$ in a sequence as arr$1[0],$ arr$1[1],....,$ arr$1[255],$ arr$2[0],$ arr$2[1],...,$ arr$2[255].($a$)$ How many paths does the function foo$()$ of this program have? Describe what they are. $($b$)$ If the cache is a direct mapped cache, how many bits in a $32-$bit address are used for block offset, set index and tag, respectively?