Design algorithm (Analysis of Algorithms in Java):

Let T be a red-black tree storing n entries, and let k be the key of an entry in T. Design an algorithm to construct from T, in O(log n) time, to two red-black trees T' and T'" such that T' contains all the keys of T less than K, and T" contains all the keys of T greater than k. Upon the completion of operation, T will be divided into T' and T".

Please explain your answer, it doesn't have to be code.