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A. Koxia and Whiteboards

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputKiyora has $$$n$$$ whiteboards numbered from $$$1$$$ to $$$n$$$. Initially, the $$$i$$$-th whiteboard has the integer $$$a_i$$$ written on it.

Koxia performs $$$m$$$ operations. The $$$j$$$-th operation is to choose one of the whiteboards and change the integer written on it to $$$b_j$$$.

Find the maximum possible sum of integers written on the whiteboards after performing all $$$m$$$ operations.

Input

Each test consists of multiple test cases. The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 1000$$$) — the number of test cases. The description of test cases follows.

The first line of each test case contains two integers $$$n$$$ and $$$m$$$ ($$$1 \le n,m \le 100$$$).

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le 10^9$$$).

The third line of each test case contains $$$m$$$ integers $$$b_1, b_2, \ldots, b_m$$$ ($$$1 \le b_i \le 10^9$$$).

Output

For each test case, output a single integer — the maximum possible sum of integers written on whiteboards after performing all $$$m$$$ operations.

Example

Input

43 21 2 34 52 31 23 4 51 110015 31 1 1 1 11000000000 1000000000 1000000000

Output

12 9 1 3000000002

Note

In the first test case, Koxia can perform the operations as follows:

- Choose the $$$1$$$-st whiteboard and rewrite the integer written on it to $$$b_1=4$$$.
- Choose the $$$2$$$-nd whiteboard and rewrite to $$$b_2=5$$$.

After performing all operations, the numbers on the three whiteboards are $$$4$$$, $$$5$$$ and $$$3$$$ respectively, and their sum is $$$12$$$. It can be proven that this is the maximum possible sum achievable.

In the second test case, Koxia can perform the operations as follows:

- Choose the $$$2$$$-nd whiteboard and rewrite to $$$b_1=3$$$.
- Choose the $$$1$$$-st whiteboard and rewrite to $$$b_2=4$$$.
- Choose the $$$2$$$-nd whiteboard and rewrite to $$$b_3=5$$$.

The sum is $$$4 + 5 = 9$$$. It can be proven that this is the maximum possible sum achievable.

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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