Consider the egg durability testing problem (again). Now you are given k identical eggs and the access to an n-floor building (floor 1 to floor n). There is a value F*, where 0 F* n such that if an egg drop from a floor higher than F*, it will break. Moreover, if an egg drops from a floor that is lower than or equal to F*, it will not break. One can conduct a series of egg drops to find out F*. A good strategy S, is strategy that always finds F* before using up all the eggs, no matter what F is. The cost of a strategy S is defined as the maximum number of drops over all possible values of F*. Give a O(nk)-time algorithm that finds the minimum-cost good strategy. It suffices to output the minimum cost rather than the entire strategy. For example, if n = 100 and k = 2, your algorithm should output 14. (a) Design an algorithm using "divide-and-conquer" approach. (b) Design an algorithm via dynamic programming.