You are given an array nums of $n$ positive integers and an integer k.

Initially, your score is $1$. You may perform the following operation at most k times:

1. Select a non empty subarray nums[l...r] where $0 \leq l \leq r < n$ that has not been previously selected.

2. Identify the element nums[i] in the subarray that has the maximum prime score. If multiple elements have the highest prime score, select the one with the smallest index i.

3. Multiply your current score by nums[i].

The prime score of an integer is defined as the number of its distinct prime factors. For instance, the prime score of $300 = 2^2 \times 3 \times 5^2$ is $3$, as its distinct prime factors are $2$, $3$, and $5$.

Return the maximum possible score achievable after applying at most k operations. Since the result may be very large, return it modulo $10^9 + 7$.

Constraints:

• $1 \leq$ nums.length $== n \leq 10^5$

• $1 \leq$ nums[i] $\leq 10^5$

• $1 \leq$ k $\leq \min(n \cdot (n + 1) / 2, 10^9)$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.