Task Assignment for Maximum Rewards

You are tasked with assigning n independent tasks to two interns under specific conditions to maximize total reward points.

Problem Description

• Each task must be completed by exactly one intern.
• For each task i:
  • If Intern 1 completes task i, you earn reward1[i] points.
  • If Intern 2 completes task i, you earn reward2[i] points.
• Intern 1 must be assigned exactly k tasks.
• Intern 2 will be assigned the remaining n - k tasks.
• Tasks can be assigned in any order; there are no contiguity requirements.

Your goal is to determine the maximum total points achievable given these constraints.

Input

• reward1: An integer array of length n, where reward1[i] is the reward if Intern 1 does task i.
• reward2: An integer array of length n, where reward2[i] is the reward if Intern 2 does task i.
• k: An integer representing the exact number of tasks Intern 1 must be assigned. It is guaranteed that 0 ≤ k ≤ n.

Output

• An integer representing the maximum possible total reward points.

Constraints and Efficiency

Design an algorithm that operates efficiently for large values of n, specifically up to 10^5.