4500: A. Ban or Pick, What's the Trick

Bobo has recently learned how to play Dota2. In Dota2 competitions, the mechanism of banning/picking heroes is introduced, modified and simplified as follows for the sake of the problem:
Suppose a game is played between two teams: Team A and Team B. Each team has a hero pool of n heroes with positive utility scores a₁,...,a_n and b₁,...,b_n, respectively. Here we assume all heroes in two teams' hero pool are distinct.The two teams then perform ban/pick operations alternately, with Team A going first. In one team's turn, it can either pick a hero for itself, or ban an unselected hero from the opponent's hero pool.
After 2n turns, all heroes are either picked or banned. Each team then needs to choose at most k heroes from all heroes it picked to form a warband and the score for the warband is calculated as the sum of utility scores over all heroes in it.
Let s_A, s_B be the score of the warband formed by Team A and Team B, respectively. Team A wants to maximize the value of s_A-s_B while Team B wants to minimize it.
Bobo wants to know, what should be the final value of s_A-s_B, if both teams act optimally? He's not really good at calculating this, so he turned to you for help.

An example of banning/picking heroes in Dota2. Source: TI10 True Sight

The first line contains two integers n,k(1<= n<= 10⁵,1<= k <= 10).
The second line contains n integers a₁,a₂,...,a_n (1<= a_i<= 10⁸), denoting the utility score of heroes for Team A.
The third line contains n integers b₁,b₂,...,b_n (1<= b_i<= 10⁸), denoting the utility score of heroes for Team B.

Output an integer in one line, denoting the answer.

2 1
3 6
2 4

2

input

4 1
1 3 5 7
2 4 6 8

output

0

input

4 2
4 6 7 9
2 5 8 10

output

3