Problem

You are given a sorted integer array in which every value appears exactly twice, except for one value that appears only once.

Return the single value that appears once.

Your solution should run efficiently, taking advantage of the sorted order rather than scanning the array linearly.

Input Format

• A sorted integer array nums of length at least 1.
• Every element appears exactly twice except one element that appears once.

Output Format

• Return the unique element that appears only one time.

Constraints

• The array is sorted in non-decreasing order.
• All values except one appear exactly twice.
• Exactly one value appears once.
• Aim for better than linear time.

Hints

• In a correctly paired sorted array, duplicate elements occupy neighboring positions.
• Consider how the position of the unique element affects the pairing structure on the left and right sides.
• Binary search can be used to check whether the current midpoint belongs to a valid pair structure.