You have N magical bags of candies in front of you. The i^th bag has A_i candies in it. It takes you one minute to finish a bag of candies, no matter how many candies are there in it. Every time you finish a bag with X candies in it, the bag is magically replenished with X/2 (rounded down to the nearest integer) more candies. The input is a sequence of integers. The first integer N is the number of bags. The next integer K is the number of minutes you have. The next N integers is the number of candies in the bags. The output of your algorithm is a single integer which represents the maximum number of candies you can eat. For the input sequence, 5, 3, 2, 1, 7, 4, 2 , the output should be 14 Write an algorithm that determines the maximum number of candies you can eat in K minutes. Explain carefully the data structure to be used and the worst case time complexity of your solution.

Please send me the solution with explanation of each line.