Maximize Subarray GCD Score

Given an array nums and up to k operations that can double distinct elements (each at most once), choose a contiguous subarray and up to k elements to double to maximize the score defined as (subarray length × GCD of its elements). With n ≤ 1500 and nums up to 1e9, the challenge is to efficiently explore subarray GCDs and the combinatorial impact of up to k single-element doublings.