### Sequence

There are two sequences of positive integers $$\{a_i\}$$ and $$\{b_i\}$$, each containing $$n$$ elements indexed $$1$$ to $$n$$. You are to choose $$K$$ integers from each sequence, out of which there must be at least $$L$$ indices which are chosen in both sequences. Given these requirements, choose these $$2K$$ integers such that their sum is maximized.

Formally, you are to choose two sets $$\{c_i\}$$ and $$\{d_i\}$$ of size K such that

• $$1 \leq c_1 < c_2 < \ldots < c_K \leq n$$
• $$1 \leq d_1 < d_2 < \ldots < d_K \leq n$$
• $$|\{c_1, c_2, \ldots, c_K\} \cap \{d_1, d_2, \ldots, d_K\}| \geq L$$
Your task is then to maximize $$\sum_{i = 1}^{K}{a_{c_i}} + \sum_{i = 1}^{K}{b_{d_i}}$$.

### Input format

The first line of input consists of a single integer $$T$$, the number of testcases.

$$T$$ testcases will follow. Each test case consists of 3 lines.

The first line of each testcase will contain 3 integers, $$n$$, $$K$$, and $$L$$.

The second line of each testcase will contain $$n$$ integers $$a_1, a_2, \ldots, a_n$$.

The third line of each testcase will contain $$n$$ integers $$b_1, b_2, \ldots, b_n$$.

### Output format

Output one line for each testcase, each containing a single integer - the maximum sum of elements as described.

### Limits

$$1 \leq T \leq 10$$.
$$1 \leq \sum{n} \leq 10^6$$.
$$1 \leq L \leq K \leq n \leq 2 \times 10^5$$
$$1 \leq a_i, b_i, \leq 10^9$$.
1 12 $$n \leq 10$$
2 8 $$n \leq 18$$
3 8 $$n \leq 30$$
4 12 $$n \leq 150$$
5 24 $$n \leq 2000$$
6 20 $$\sum{n} \leq 3 \times 10^5$$

### Samples

 Sample Input 1 Sample Output 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 1412274562

The optimal solution for the first testcase is $$\{c_i\} = \{d_i\} = \{1\}$$.
An optimal solution for the second testcase is $$\{c_i\} = \{1, 3\}, \{d_i\} = \{2, 3\}$$.
The optimal solution for the third testcase is $$\{c_i\} = \{3, 4\}, \{d_i\} = \{3, 5\}$$.
The optimal solution for the fourth testcase is $$\{c_i\} = \{d_i\} = \{2, 3, 4, 6\}$$.
The optimal solution for the fifth testcase is $$\{c_i\} = \{2, 3, 4, 5, 6\}, \{d_i\} = \{1, 2, 3, 4, 6\}$$.

### Compile Errors

Time Limit: 1 Seconds
Memory Limit: 1024MB
No. of ACs: 1