## Problem Implement `largest_positive_and_subset(nums)`. Choose a nonempty subset of the given nonnegative integers. The subset is valid when the bitwise AND of all selected values is strictly positive. Return the largest possible subset size. If no valid subset exists, return `0`. ## Constraints - `1 <= len(nums) <= 200,000` - `0 <= nums[i] < 2^31` - Elements are selected by index, so duplicate values count as separate choices. - The selected elements do not need to be contiguous. ## Clarifications The bitwise AND must be greater than zero, not merely nonnegative. You only need the maximum size, not the subset itself. ## Examples `[5, 3, 10, 7]` returns `3`. For example, `5`, `3`, and `7` all have their least-significant bit set, so their AND is positive. `[0, 0, 0]` returns `0`. `[6, 14, 2, 7]` returns `4` because all four values have the bit with value `2` set, so their combined AND is positive. ## Hint If an AND result is positive, at least one bit survives in every selected value. Turn that observation into a counting problem over bit positions. ## Interview Follow-ups - Return one maximum subset of indices. - Generalize the requirement so the AND must contain at least two set bits. - Explain why enumerating subsets is unnecessary.