Bessie's grades this year are... questionable.
The school year is divided into two semesters. Bessie's scores on assignments in each semester can be represented as integer sequences $$$a_1, a_2, \ldots, a_n$$$ and $$$b_1, b_2, \ldots, b_m$$$ of length $$$n$$$ and $$$m$$$ respectively.
Bessie's grade for a semester is the average of all her scores in that semester. Her overall grade is the average of her semester grades. Here, the average of an integer sequence $$$x_1, x_2, \ldots, x_l$$$ of length $$$l$$$, is $$$\frac{x_1+x_2+\ldots+x_l}{l}$$$. Note that this value may not necessarily be integer.
Bessie has hacked into the school's computers, and can do the following operation at most $$$k$$$ times without raising suspicion:
At the end, both semesters should have at least one score. Help Bessie find the maximum overall grade she can achieve!
Input consists of multiple tests. The first line contains $$$t$$$, the number of tests ($$$1 \le t \le 10^4$$$).
The first line of each test contains $$$n$$$, $$$m$$$, and $$$k$$$ — the number of scores in each semester, and the maximum number of operations ($$$1 \le n, m \le 10^5$$$, $$$0 \le k \le n+m$$$).
The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$, Bessie's scores in the first semester ($$$1 \le a_i \le 10^9$$$).
The third line contains $$$m$$$ integers $$$b_1, b_2, \ldots, b_m$$$, Bessie's scores in the second semester ($$$1 \le b_i \le 10^9$$$).
It is guaranteed the sum of $$$n + m$$$ over all tests does not exceed $$$2 \cdot 10^5$$$.
For each test, output a floating-point number, the maximum overall grade Bessie can achieve.
Your answer is considered correct if its absolute or relative error does not exceed $$$10^{-6}$$$.
Formally, let your answer be $$$a$$$, and the jury's answer be $$$b$$$. Your answer is accepted if and only if $$$\frac{|a - b|}{\max{(1, |b|)}} \le 10^{-6}$$$.
In tests worth $$$50$$$ points, it is guaranteed that $$$1 \le n, m \le 100$$$.
32 5 06 11 1 1 1 12 5 16 11 1 1 1 16 9 49 2 15 1 13 1110 3 4 7 5 8 6 14 12
2.25 3.5 10.538461538461538
In the first test, Bessie can't do anything. So her grade for the first semester is $$$\frac{6+1}{2}=3.5$$$, and her grade for the second semester is $$$\frac{1+1+1+1+1}{5} = 1$$$. Averaging these gives an overall grade of $$$\frac{1+3.5}{2}=2.25$$$.
In the second test, it is optimal to move the score of $$$1$$$ in the first semester to the second semester. Then, the averages for each semester become $$$6$$$ and $$$1$$$, resulting in an overall grade of $$$\frac{6+1}{2}=3.5$$$.
