A15855. Hot Start Up (easy version)

This is an easy 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 consists of multiple test cases. The first line contains a single integer $t$ , the number of test cases ( $1 \le t \le 5000$ ).

The first line of each test case contains $n$ and $k$ ( $1 \le n, k \le 5000$ ).

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 $5000$ .

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

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.