Find max consecutive elements with sum below target

You are given: - An integer array `nums` of length `n`, sorted in non-decreasing order. - An integer `index` such that `0 ≤ index < n`. - An integer `target`. Starting from position `index`, you may take a contiguous sequence of elements going to the right: `nums[index], nums[index + 1], ..., nums[index + k - 1]` for some integer `k ≥ 0`. You want the sum of the chosen elements to be **strictly less than** `target`: \[ \sum_{i=index}^{index + k - 1} nums[i] < target. \] Find the **maximum possible value of `k`** (the maximum number of consecutive elements starting from `index` whose sum is `< target`). If even `nums[index] ≥ target`, then the answer should be `0`. Design an efficient algorithm to compute this maximum `k`. You may assume: - `1 ≤ n` - `nums` is sorted in non-decreasing order. Describe the algorithm you would implement and its time and space complexity.