Window with the most copies of a target value

Implement most_target_window(nums, target_index, window_size).

The target value is nums[target_index]. Look at every contiguous subarray of nums with exactly window_size elements. Return the starting index of the one that contains the target value the most times. If several windows tie, return the smallest starting index.

The answer window does not need to include position target_index.

Input

• nums: a list of integers, 1 <= len(nums) <= 10^5.
• target_index: an index into nums.
• window_size: the window length, 1 <= window_size <= len(nums).

Return -1 if the input is invalid (empty array, target_index out of range, or window_size outside [1, len(nums)]).

Aim for O(n) time and O(1) extra space.

Example 1

nums = [4, 7, 1, 4, 4, 4, 2], target_index = 0, window_size = 3
target = 4
copies of 4 per window start: 0->1, 1->1, 2->2, 3->3, 4->2
answer: 3   (window [4, 4, 4])

Example 2

nums = [1, 2, 1, 2], target_index = 0, window_size = 2
target = 1
every window holds one 1
answer: 0   (tie, smallest start)

Reconstructed from the reported question; details may differ from what interviewers ask.