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