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A min-heap is useful when we are interested in the minimum value of a set of numbers. Now, instead of the min, we are interested

A min-heap is useful when we are interested in the minimum value of a set of numbers. Now, instead of the min, we are interested in the K-th smallest value. a.) Please design a data structure to allow the following two operations: push (insert a new number) and find_Kmin (return the value of the K-th smallest number without removing it). Both operations should be done in O(log K) time. b.) In addition to push and find_Kmin, now we also want to support the pop operation to return and remove the K-th smallest element. Please design a data structure to support these three operations, and each operation should take O(log n) time with n being the size of the current set.

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