Given two positive integer sequences ~\{a_1, a_2, \dots, a_n\}~ and ~\{b_1, b_2, \dots, b_n\}~ of length ~n~, you must find two sequences ~\{c_1, c_2, \dots, c_K\}~ and ~\{d_1, d_2, \dots, d_K\}~ of length ~K~ satisfying the following conditions:

1. ~1 \le c_1 < c_2 < \dots < c_K \le n~.
2. ~1 \le d_1 < d_2 < \dots < d_K \le n~.
3. ~|\{c_1, c_2, \dots, c_K\} \cap \{d_1, d_2, \dots, d_K\}| \ge L~.

Subject to these conditions, maximize ~\sum_{i=1}^K a_{c_i} + \sum_{i=1}^K b_{d_i}~.

Input Specification

The first line contains an integer ~T~, indicating the number of test cases.

For each test case:

The first line contains three integers ~n~, ~K~, ~L~.

The second line contains ~n~ integers, indicating ~\{a_1, a_2, \dots, a_n\}~.

The third line contains ~n~ integers, indicating ~\{b_1, b_2, \dots, b_n\}~.

Constraints

For all test cases, ~T \le 10~, ~1 \le \sum n \le 10^6~, ~1 \le L \le K \le n \le 2 \times 10^5~, ~1 \le a_i,b_i \le 10^9~.

Test Case	~n \le~	~\sum n \le~
1~3	~10~	~3 \times 10^5~
4~5	~18~
6~7	~30~
8~10	~150~
11~16	~2\,000~
17~21	~2 \times 10^5~
22~25		~10^6~

Output Specification

Output one integer on one line, the answer.

Sample Input 1

5
1 1 1
7
7
3 2 1
4 1 2
1 4 2
5 2 1
4 5 5 8 4
2 1 7 2 7
6 4 1
1 5 8 3 2 4
2 6 9 3 1 7
7 5 4
1 6 6 6 5 9 1
9 5 3 9 1 4 2

Sample Output 1

14
12
27
45
62