You are given an integer array nums and two integers a and b.

A subarray is considered valid if:

• It contains at least $1$ odd integer.

• The ratio of the number of even integers to the number of odd integers in the subarray is at most $\frac{a}{b}$, which means that the number of even integers multiplied by b is less than or equal to the number of odd integers multiplied by a.

Return the total number of valid subarrays of nums.

Constraints:

• $1 \leq$ nums.length $\leq 1000$

• $1 \leq$ nums[i] $\leq 1000$

• $1 \leq$ a, b $\leq 1000$

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.