Contiguous Subarray Product Less Than K

You are given an array of positive integers and a positive integer \( k \). Your task is to find the number of contiguous subarrays where the product of all the elements is strictly less than \( k \). This problem tests your ability to use the sliding window technique efficiently.

Example:

Input: [10, 5, 2, 6], k = 100
Output: 8
Explanation:
The contiguous subarrays that have a product less than 100 are:
[10], [5], [2], [6], [10,5], [5,2], [2,6].

</p>

Note: If \( k \) is less than or equal to 1, there will be no valid subarray because all numbers are at least 1.

inputFormat

The first line of input contains an integer \( n \) denoting the number of elements in the array.

The second line contains \( n \) space-separated positive integers representing the array.

The third line contains an integer \( k \).

outputFormat

Output a single integer, the number of contiguous subarrays where the product of all the elements is less than \( k \).

## sample

4
10 5 2 6
100

8