Given the following memory status, determine the memory locations to which three processes $P_1,P_2,$ and $P3,$ requiring $2K,4K,$ and $9K$ of contiguous memory, respectively, should be allocated based on $($i$)$ First$-$fit strategy and $($ii$)$ Worst$-$fit strategy. You must first allocate memory to $P1,$ then to $P2,$ and finally to $P3.$ Show the status of the memory after the allocation for all three processes in each case. Current memory status: $0-12K$ allocated; $12$K$-14$K: Free; $14$K$-30$K allocated; $30K-38K$ Free; $38K-45K$ allocated; $45K-50K$ Free.