i$)$ Develop well$-$documented pseudo code that finds all two elements $($non$-$negative numbers$)$ a and b of a given array that modulo up precisely to a given value x$,$ that is$,$ a $\%$ b $=$ x$.$ The code must display the indices and the values of these elements. For instance, given the following array $(123,73,39,12,14,9,113,93,203,22,25,10)$ and x as $3,$ your code should find and display something similar to the following $($notice that this is just an example. Your solution must not refer to this particular example$).$ Notice that the output should show all possible pairs: a$.$ All pairs of elements of the array that modulo to a value of $3$ are: b$.$ Indices $0$ & $3$ with values $123$ & $12($e$.$g$.,123\%12$ returns $3)$ c$.$ Indices $1$ & $4$ with values $73$ & $14$ d$.$ Indices $2$ & $5$ with values $39$ & $9$ e$.$ Indices $6$ & $9$ with values $113$ & $22$ f$.$ etc. ii$)$ Briefly justify the motive$($s$)$ behind your design. iii$)$ What is the Big$-$O time and space complexity of your solution? Explain clearly how you obtained such complexity.