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. $1\le c_1<c_2<\cdots <c_K\le n$.
2. $1\le d_1<d_2<\cdots <d_K\le n$.
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	$2000$
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