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#### DreamTeam

Divide developers into two teams to maximize their total contribution.

A company has employed N developers (numbered from 0 to N−1) and wants to divide them into two teams. The first is a front-end team with F developers. The second is a back-end team with N−F developers. If the K-th developer is assigned to the front-end team then their contribution is A[K], and if they are assigned to the back-end team then their contribution is B[K]. What is the maximum sum of contributions the company can achieve?

Write a function:

class Solution { public int solution(int[] A, int[] B, int F); }

that, given two arrays A, B (consisting of N integers each) and the integer F, returns the maximum sum of contributions the company can achieve.

Examples:

1. Given A = [4, 2, 1], B = [2, 5, 3] and F = 2, the function should return 10. There should be two front-end developers and one back-end developer. The 0th and 2nd developers should be assigned to the front-end team (with contributions 4 and 1) and the 1st developer should be assigned to the back-end team (with contribution 5).

2. Given A = [7, 1, 4, 4], B = [5, 3, 4, 3] and F = 2, the function should return 18. The 0th and 3rd developers should be assigned to the front-end team and the 1st and 2nd developers should be assigned to the back-end team.

3. Given A = [5, 5, 5], B = [5, 5, 5] and F = 1, the function should return 15. The 0th developer can be assigned to the front-end team and the 1st and 2nd developers can be assigned to the back-end team.

Write an efficient algorithm for the following assumptions:

• N is an integer within the range [1..200,000];
• arrays A and B have equal lengths;
• each element of array A is an integer within the range [0..1,000];
• F is an integer within the range [0..N].