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We are given an array that contains $N$ numbers. We want to determine if there are two numbers whose sum equals a given number $K.$ For instance, if the input is $8,4,1,6$ and $K$ is $10,$ then the answer is yes $(4$ and $6).$ A number may be used twice.

Select one or more:

a$.$ If the elements are first sorted with mergesort, then the total cost of the solving algorithm is $0(\frac{N}{logN})$

b$.$ It the elements are first sorted with insertion sort, then the total cost of the solving algorithm is $O(N^{2}logN)$

c$.$ A bruie$-$force search algorithm costs O$($N$2)$

d$.$ A brute$-$force search algonithm costs $0(N^3)$