Consider the following multi$-$dictionary problem. Let A$[1..$ n$]$ be a fixed array of distinct integers. Given an array X $[1..$ k$],$ we want to find the position $($if any$)$ of each integer X$[$i$]$ in the array A$.$ In other words, we want to compute an array I$[1..$k$]$ where for each i$,$ either I$[$i$]=0($so zero means $$none$)$ or A$[$I$[$i$]]=$ X$[$i$].$ Determine the exact complexity of this problem, as a function of n and k$,$ in the binary decision tree model.