The Growth Constraint

In a lab, a bacterial culture's growth factor is measured hourly as a sequence of positive integers. To prevent an explosion, the product of growth factors in any observation period must not exceed a limit P. Find the length of the longest contiguous observation period that satisfies this constraint. Input Format: - The first line contains two integers: P (the product limit) and N (the number of hours). - The second line contains N space-separated positive integers. Output Format: - Print a single integer representing the length of the longest valid period. Example: Input: 20 5 2 3 2 5 2 Output: 3 Explanation: The period [2, 3, 2] has a product of 12 (<= 20). [2, 5, 2] has a product of 20 (<= 20). Both are length 3.