A school has a total of $3 * n$ students, divided evenly into $A$ group, $B$ group or $C$ group, with $n$ in each group. Everyone has an ability value $v_i$, the tacit value between two students is $f (i, j) = (v_i + v_j) * (v_i plus.circle v_j) % M$, where $plus.circle$ means bitwise exclusive OR operation. As the competition coach of this school, you need to select exactly $m$ teams to participate in the $C C P C$ competition in the second half of the year.
Specifically, Each team contains exactly three students, and the three students are from different groups. Let the team members from the $A, B, C$ group be $a, b, c$, then the tacit value of this team is $f (a, b) + f (a, c)$.
Please find out the maximum sum of the tacit values of the $m$ teams.
The input consists of multiple test cases.
The first line contains an integer $T$ $(1 <= T <= 10)$ — the number of test cases. The description of the test cases follows.
The first line contains three integers $n, m, M$ $(1 <= m <= n <= 200, 10 <= M <= 2000)$.
Then follows three lines, each line contains $n$ integers $v_1, v_2, \\dots, v_n$ $(1 <= v_i <= 2000)$ — the ability value of each student in group $A, B$ and $C$ .
For each test case, print the answer.
## Input
The input consists of multiple test cases. The first line contains an integer $T$ $(1 <= T <= 10)$ — the number of test cases. The description of the test cases follows.The first line contains three integers $n, m, M$ $(1 <= m <= n <= 200, 10 <= M <= 2000)$.Then follows three lines, each line contains $n$ integers $v_1, v_2, \\dots, v_n$ $(1 <= v_i <= 2000)$ — the ability value of each student in group $A, B$ and $C$ .
## Output
For each test case, print the answer.
[samples]
**Definitions**
Let $ n, k_1, k_2 \in \mathbb{Z} $ with $ 1 \leq n \leq 10^6 $, $ 0 \leq k_1, k_2 \leq 2^{64} - 1 $.
Let $ A = (a_1, a_2, \dots, a_n) $ be a sequence of distinct positive integers generated by a deterministic function $ \texttt{gen()} $ using seeds $ k_1, k_2 $.
Let $ Q \in \mathbb{Z} $ with $ 1 \leq Q \leq 5 \cdot 10^5 $ be the number of commands.
**Commands**
Each command is a tuple $ (\text{op}, x) $ where $ \text{op} \in \{ \texttt{F}, \texttt{D}, \texttt{C}, \texttt{R} \} $, $ x \in \mathbb{Z} $, $ 1 \leq x \leq 10^{12} - 1 $.
- **F (Find)**: Find the smallest index $ i $ such that $ a_i \geq x $. Output $ a_i $ if exists, else output $ -1 $.
- **D (Delete)**: Remove $ a_i $ from $ A $ where $ a_i = x $ (guaranteed to exist).
- **C (Count)**: Count the number of elements $ a_i \in A $ such that $ a_i \leq x $.
- **R (Reset)**: Reset $ A $ to its original state (generated by $ \texttt{gen()} $ with initial $ k_1, k_2 $).
**Constraints**
1. All $ a_i $ are distinct.
2. Number of $ \texttt{R} $ commands $ \leq 10 $.
**Objective**
For each command $ \texttt{F} $ and $ \texttt{C} $, output the required value immediately.
For $ \texttt{D} $ and $ \texttt{R} $, update the state of $ A $ accordingly.