Allocate Minimum Number of Pages

Hard

Problem Statement

Given an array of integers pages representing the number of pages in n books and a number of students k, allocate the books to k students such that each student gets at least one book, all books are assigned, and each assignment is a contiguous block of books. The goal is to minimize the maximum number of pages assigned to any single student.

Examples

1Example 1

Input:

{
  "pages": [
    12,
    34,
    67,
    90
  ],
  "k": 2
}

Output:

113

2Example 2

Input:

{
  "pages": [
    10,
    20,
    30,
    40
  ],
  "k": 2
}

Output:

60

3Example 3

Input:

{
  "pages": [
    10,
    5,
    20
  ],
  "k": 2
}

Output:

20