Selectionsort takes time $($rougly$)$ proportional to n$2$ while mergesort takes time $($roughly$)$ proportional to nlogn$,$ where n is the array size. Suppose that both algorithms take the same amount of time to sort an array of size $100.$ What will be the ratio of the runtimes selectionsort $/$ mergesort when the array size is increased to

a$)10,000\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

b$)100,000,000?\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

Justify your answers using the applicable rules of thumb.