Apply Operations to Maximize Score

Given nums and k, each operation picks an unused subarray and multiplies the score by the element in that subarray with the largest number of distinct prime factors (ties broken by smaller index); maximize the final product mod 1e9+7 after at most k operations. The algorithmic core is computing for each element how many subarrays would select it as the prime-score winner (with tie-break), typically via a monotonic-stack range-count, then greedily using those counts to pick the largest values up to k multiplications.