Given a sorted array of distinct positive integers arr and an integer k, find the k-th positive integer that does not appear in the array. Every position in the array hides a count: at index i (0-indexed), if no positive integer were missing, arr[i] would equal i + 1 exactly. The gap between them — arr[i] - (i + 1) — is exactly how many positive integers are missing among the first i + 1 array slots. That gap only ever grows (or stays flat) moving rightward through the array, which makes this a binary search on the answerBinary Search on the AnswerThe search runs directly over the space of candidate answers rather than over the array's values. It applies whenever a derived quantity — here, the count of missing numbers so far — only ever increases (or only decreases) as the search position moves in one direction.: binary search finds the boundary index where the missing count first reaches k, and the answer follows directly from that boundary.