Kevin has an integer sequence $$$a$$$ of length $$$n$$$. At the same time, Kevin has $$$m$$$ types of magic, where the $$$i$$$-th type of magic can be represented by an integer $$$b_i$$$.

Kevin can perform at most $$$k$$$ (possibly zero) magic operations. In each operation, Kevin can do the following:

- Choose two indices $$$i$$$ ($$$1\leq i\leq n$$$) and $$$j$$$ ($$$1\leq j\leq m$$$), and then update $$$a_i$$$ to $$$a_i\ \&\ b_j$$$. Here, $$$\&$$$ denotes the bitwise AND operation.

Find the minimum possible sum of all numbers in the sequence $$$a$$$ after performing at most $$$k$$$ operations.

Input format:
Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). The description of the test cases follows.

The first line of each test case contains three integers $$$n, m, k$$$ ($$$1\leq n \leq 10^5$$$, $$$1\leq m \leq 10$$$, $$$0\leq k\leq nm$$$) — the length of $$$a$$$, the number of types of magic, and the maximum number of operations.

The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$0\leq a_i < 2^{30}$$$).

The third line contains $$$m$$$ integers $$$b_1, b_2, \ldots, b_m$$$ ($$$0\leq b_i < 2^{30}$$$).

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^5$$$.
Output format:
For each test case, output one integer — the minimum possible sum of all numbers in the sequence $$$a$$$ after performing at most $$$k$$$ operations.
Example Input 0:
5
1 3 2
7
5 6 3
2 3 2
5 6
5 6 3
10 2 5
3 1 4 1 5 9 2 6 5 3
7 8
5 1 0
1073741823 1073741823 1073741823 1073741823 1073741823
1073741823
1 1 0
0
0

Example Output 0:
1
3
11
5368709115
0

Notes:
In the first test case, one possible way could be:

- Update $$$a_1$$$ to $$$a_1\ \&\ b_1$$$. The sequence will become $$$[5]$$$.
- Update $$$a_1$$$ to $$$a_1\ \&\ b_3$$$. The sequence will become $$$[1]$$$.

In the second test case, one possible way could be:

- Update $$$a_1$$$ to $$$a_1\ \&\ b_3$$$. The sequence will become $$$[1, 6]$$$.
- Update $$$a_2$$$ to $$$a_2\ \&\ b_3$$$. The sequence will become $$$[1, 2]$$$.

Example input:
5
1 3 2
7
5 6 3
2 3 2
5 6
5 6 3
10 2 5
3 1 4 1 5 9 2 6 5 3
7 8
5 1 0
1073741823 1073741823 1073741823 1073741823 1073741823
1073741823
1 1 0
0
0


Example output:
1
3
11
5368709115
0