You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 1.0 seconds
Memory limit: 512.0 MB

# Problem
This is a hard version of the problem. The constraints of $$$t$$$, $$$n$$$, $$$k$$$ are the only difference between versions.

You have a device with two CPUs. You also have $$$k$$$ programs, numbered $$$1$$$ through $$$k$$$, that you can run on the CPUs.

The $$$i$$$-th program ($$$1 \le i \le k$$$) takes $$$cold_i$$$ seconds to run on some CPU. However, if the last program we ran on this CPU was also program $$$i$$$, it only takes $$$hot_i$$$ seconds ($$$hot_i \le cold_i$$$). Note that this only applies if we run program $$$i$$$ multiple times consecutively  — if we run program $$$i$$$, then some different program, then program $$$i$$$ again, it will take $$$cold_i$$$ seconds the second time.

You are given a sequence $$$a_1, a_2, \ldots, a_n$$$ of length $$$n$$$, consisting of integers from $$$1$$$ to $$$k$$$. You need to use your device to run programs $$$a_1, a_2, \ldots, a_n$$$ in sequence. For all $$$2 \le i \le n$$$, you cannot start running program $$$a_i$$$ until program $$$a_{i - 1}$$$ has completed.

Find the minimum amount of time needed to run all programs $$$a_1, a_2, \ldots, a_n$$$ in sequence.

## Input Format
Input consists of multiple test cases. The first line contains a single integer $$$t$$$, the number of test cases ($$$1 \le t \le 10^5$$$).

The first line of each test case contains $$$n$$$ and $$$k$$$ ($$$1 \le n, k \le 3 \cdot 10^5$$$).

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

The third line of each test case contains $$$k$$$ integers $$$cold_1, cold_2, \ldots, cold_k$$$ ($$$1 \le cold_i \le 10^9$$$).

The fourth line of each test case contains $$$k$$$ integers $$$hot_1, hot_2, \ldots, hot_k$$$ ($$$1 \le hot_i \le cold_i$$$).

It is guaranteed the sum of $$$n$$$ and the sum of $$$k$$$ over all test cases do not exceed $$$3 \cdot 10^5$$$.

## Output Format
For each test case, print the minimum time needed to run all programs in the given order.

## Examples
```input
9
3 2
1 2 2
3 2
2 1
4 2
1 2 1 2
5 3
2 1
4 3
1 2 3 1
100 100 100
1 1 1
5 2
2 1 2 1 1
65 45
54 7
5 3
1 3 2 1 2
2 2 2
1 1 1
5 1
1 1 1 1 1
1000000000
999999999
5 6
1 6 1 4 1
3 6 4 1 4 5
1 1 1 1 4 1
1 3
3
4 5 6
1 2 3
8 3
3 3 3 1 2 3 2 1
10 10 8
10 10 5
```
```output
6
11
301
225
8
4999999996
11
6
63
```

## Note
In the first test case, we can do the following:

- Run program $$$a_1 = 1$$$ on CPU $$$1$$$. It takes $$$cold_1 = 3$$$ seconds to run.
- Run program $$$a_2 = 2$$$ on CPU $$$2$$$. It takes $$$cold_2 = 2$$$ seconds to run.
- Run program $$$a_3 = 2$$$ on CPU $$$2$$$. The last program run on this CPU was also program $$$2$$$, so it takes $$$hot_2 = 1$$$ second to run.

In total, we need $$$3 + 2 + 1 = 6$$$ seconds to run them all. We can show this is optimal.

In the second test case, we can use do the following:

- Run program $$$a_1 = 1$$$ on CPU $$$1$$$. It takes $$$cold_1 = 5$$$ seconds to run.
- Run program $$$a_2 = 2$$$ on CPU $$$2$$$. It takes $$$cold_2 = 3$$$ seconds to run.
- Run program $$$a_3 = 1$$$ on CPU $$$1$$$. The last program run on this CPU was also program $$$1$$$, so it takes $$$hot_1 = 2$$$ seconds to run.
- Run program $$$a_4 = 2$$$ on CPU $$$2$$$. The last program run on this CPU was also program $$$2$$$, so it takes $$$hot_2 = 1$$$ second to run.

In total, we need $$$5 + 3 + 2 + 1 = 11$$$ seconds. We can show this is optimal.

Now solve the problem and return the code.