Maintain streaming median and loosemedian

Design a data structure for an online stream of positive integers supporting insert (x). After each insertion, output: (a) the median of all values seen so far (for an even count, define the median as the average of the two middle values); and (b) the 'loose median' interval [2^k, 2^(k+ 1)] where k is the unique integer satisfying 2^k < median < 2^(k+ 1). Describe the algorithms and data structures, their time and space complexities, and how to implement bit operations to compute 2^k from the median. Discuss how you would handle boundary cases (e.g., median equals a power of two, zero/negative numbers, or non-integer medians).