You are working as a programmer for UMass administration, and they ask you to determine the median GPA for all students. However, student GPAs are stored in two different databases, one for in-state students and one for out-of-state students. Assume there are n students of each type, so there are 2n students total. Youd like to determine the median of this set of 2n values, which we will define here to be the nth smallest value. (Note: this is the definition of the median for the purposes of this problem. Consider it carefully and ignore other definitions you may know.) However, security is very tight, so the only way you can access these values is through queries to the databases. In a single query, you can specify a value k to one of the two databases, and the chosen database will return the kth smallest value that it contains. Since queries are expensive, you would like to compute the median using as few queries as possible. Give an algorithm that finds the median value using at most O(log n) queries.