Subarrays Product Less Than K

AlphaGrep Securities monitors contiguous runs of positive integer signals and needs to count how many have a combined product below a threshold. Given an array nums of positive integers and an integer k, return the number of contiguous, non-empty subarrays whose product is strictly less than k.

Formal Specification

Implement num_subarray_product_less_than_k(nums, k).

• Input: nums, a list of positive integers, and k, a positive integer.
• Output: An integer representing the number of non-empty contiguous subarrays whose product is less than k.
• Each element must be used according to its position, and subarrays must be contiguous.