at any point during the binary search algorithm, we consider, as usual, a range (l...,r) of the suffix array and its central point m, and decide whether we continue our search in the left sub-range (l...,m) or in the right sub-range (m...,r). in order to make the decision, we compare p to the string at m. if p is identical to m, search is complete. but if not, we have already compared the first k characters of p and then decided whether p is lexicographically smaller or larger than m. let's assume the outcome is that p is larger than m. so, in the next step, we consider (m...,r) and a new central point m' in the middle: