Find smallest start index avoiding left exit

You are given an integer array `jump` of length `n` (0-indexed). If you are currently at index `i`, your next position becomes `i + jump[i]` (a positive value moves right, a negative value moves left). Starting from an index `s`, you repeatedly apply this move rule. - If you ever reach an index `< 0`, you have moved out of the **left boundary**. - If you reach an index `>= n`, you have moved out of the array on the right (you may treat this as stopping). - The process may also loop inside the array. Return the **smallest** starting index `s` such that, during the entire process starting from `s`, you **never** move out of the left boundary (i.e., the sequence of visited indices never becomes negative). If no such index exists, return `-1`. Implement an algorithm that runs in O(n) time if possible.