Given two sensor logs, logA and logB, each already sorted in non-decreasing order (possibly empty, but never both at once), and an integer k, find the k-th smallest reading across both logs combined — without actually merging them into one list first. The direct approach merges the two logs (an easy O(m+n) two-pointer walk, since both are already sorted) and then simply reads off the value at index k-1. That works, but it builds the entire merged log even though only one position in it is ever needed — wasteful once the logs get large. The faster approach reuses the same partition binary searchBinary Search on the PartitionInstead of searching over array values or over a range of candidate answers, this binary search hunts for a cut position (an index) in the shorter array. A cut is valid once every value kept on its left side is ≤ every value kept on its right side across both arrays combined — exactly the ordering a real merge would produce, found without ever performing the merge. idea used to find a combined median: search for the one cut position across both logs whose left side holds exactly the first k combined values, with every left value ≤ every right value. Once that cut is found, the k-th smallest reading is read directly off its boundary — in O(log(min(m, n))) time, without merging anything.