How to Solve Apply Operations to Maximize Score Problem

You are given an array nums of n positive integers and an integer k. Initially, you start with a score of 1. You have to maximize your score by applying the following operation at most k times: Here, nums[l, ..., r] denotes the subarray of nums starting at index l and ending at the index r, both ends being inclusive. The prime score of an integer x is equal to the number of distinct prime factors of x. For example, the prime score of 300 is 3 since 300 = 2 * 2 * 3 * 5 * 5. Return the maximum possible score after applying at most k operations. Since the answer may be large, return it modulo 109 + 7.