Minimize Maximum Partition Sum

Problem Statement

Given an array of positive integers and an integer k, partition the array into exactly k non-empty contiguous subarrays. Your task is to partition the array such that the largest sum among these subarrays is minimized. Return that minimized maximum sum.

Input

• An array of positive integers, for example: arr = [7, 2, 5, 10, 8]
• A positive integer k representing the number of subarrays.

Output

• A single integer: the minimized maximum subarray sum achievable by partitioning the array as required.

Example

For arr = [7, 2, 5, 10, 8] and k = 2, one valid partition is [7, 2, 5] and [10, 8], with subarray sums 14 and 18 respectively. The answer would be 18 as it is the smallest possible maximum sum among all valid partitions.

Constraints

• Every element in the array is a positive integer.
• k is a positive integer and is at most the length of the array.
• The array can be large, so an efficient solution is expected.

Note

The partition must keep the order of elements as in the original array.

Implement a function or method to solve this problem. Ensure your code is clean, efficient, and well-documented.