D. Where's My Money?
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

After struggling with plan choosing in One Must Imagine Time Tight, OC, KP, and XW decided to settle things a different way: by splitting bills.

Everyone likes AA, which means that all bills are split equally, but it is really inconvenient to pay separately every time they check out. Therefore, they decided that one person would pay all the bills upfront each time and share the total amount in a WeChat group, and they would settle up together after returning to school.

Fortunately, they all travel in groups of three, so it's guaranteed that no two people split the bills separately.

However, the journey back from the other world was exhausting, and the three returned to school feeling drained and unable to struggle with the accounts. Can you help them?

Formally, given $$$3$$$ arrays of floating-point numbers $$$a, b, c$$$, denoting the lists of bills paid by OC, KP, and XW respectively, for any two different people $$$A$$$ and $$$B$$$, output the amount $$$A$$$ needs to transfer to $$$B$$$ so that in the end, everyone has split the bills equally.

You do not need to minimize the total sum of all money transfers. In other words, meaningless transfers are allowed.

Input

There are multiple test cases. The first line of the input contains an integer $$$t$$$ $$$(1 \leq t \leq 100)$$$, denoting the number of test cases. For each test case:

The first line contains three integers $$$n, m, p$$$ $$$(0 \leq n, m, p \leq 10 ^ 3)$$$.

The second line contains $$$n$$$ positive floating-point numbers $$$a_i$$$ $$$(0 \lt a_i \leq 10 ^ 3)$$$, denoting the lists of bills paid by OC.

The third line contains $$$m$$$ positive floating-point numbers $$$b_i$$$ $$$(0 \lt b_i \leq 10 ^ 3)$$$, denoting the lists of bills paid by KP.

The fourth line contains $$$p$$$ positive floating-point numbers $$$c_i$$$ $$$(0 \lt c_i \leq 10 ^ 3)$$$, denoting the lists of bills paid by XW.

It's guaranteed that the decimal places of the floating-point numbers do not exceed $$$2$$$.

Output

Define $$$A \rightarrow B$$$ as the amount $$$A$$$ needs to transfer to $$$B$$$.

For each test case, output one line containing $$$6$$$ floating-point numbers, denoting the amounts that: OC $$$\rightarrow$$$ KP, OC $$$\rightarrow$$$ XW, KP $$$\rightarrow$$$ OC, KP $$$\rightarrow$$$ XW, XW $$$\rightarrow$$$ OC, XW $$$\rightarrow$$$ KP.

Note that negative amounts of transfer are not allowed.

Your answer will be accepted if after transferring, the absolute error between every two people's payment does not exceed $$$10^{-2}$$$.

Example
Input
2
7 2 1
90.11 15 318 25.67 7.71 57.55 40.96
10 81
33.9
1 1 1
100
100
100
Output
0.00 0.00 154.67 0.00 173.70 19.03 
0.00 0.00 0.00 0.00 0.00 0.00
Note

For the first sample test case, the total amount of payment is $$$679.9$$$, and the optimal choice is $$$KP \rightarrow OC = 135.63, XW \rightarrow OC = 192.73$$$. But you do not need to minimize the total amount of transfers, so the sample given is also acceptable.

For the second sample test case, everyone has exactly split the bills equally, so no one owes anyone else.