Book Allocation: Minimize Maximum Pages

You are given a list of positive integers pages, where pages[i] is the number of pages in the i-th book, and an integer students (k). The books must be allocated to exactly k students such that: - Each student gets at least one book. - Each student gets a contiguous block of books (i.e., the books are in a fixed order and are divided into k contiguous subarrays). - Each book is assigned to exactly one student. Your task is to implement the function `min_max_pages(pages: list[int], students: int) -> int` which returns the minimum possible value of the maximum total pages assigned to any student. If it is impossible to allocate the books to k students (e.g., k > number of books), return -1. The allocation must be contiguous, meaning the order of books cannot be changed. For example, given pages = [12, 34, 67, 90] and students = 2, possible allocations are: - [12] and [34, 67, 90] => max = 191 - [12, 34] and [67, 90] => max = 157 - [12, 34, 67] and [90] => max = 113 Thus, the answer is 113. Implement the function accordingly.

>>> min_max_pages([12, 34, 67, 90], 2)
113
>>> min_max_pages([5, 10, 30, 20, 15], 3)
35
>>> min_max_pages([10, 20, 30], 1)
60
>>> min_max_pages([10, 20, 30], 5)
-1
>>> min_max_pages([], 1)
-1