시간 제한메모리 제한제출정답맞힌 사람정답 비율
5 초 256 MB269836.364%

## 문제

$\text{Let}~t = n/m;~~~z\left[ t \right] =\begin{cases} (a+(b+rt^{ 2 })z\left[ -1-2t \right] )/r & \text{ if }~ t\le 0 \\ (c+(d+rt^{ 2 })z\left[ 1-2t \right] )/r & \text{if}~t > 0 \end{cases}$

Given integer $$a$$, $$b$$, $$c$$, $$d$$, $$n$$, $$m$$, and $$r$$, evaluate $$z\left[ t \right]$$ (as a floating point number).

$1 \le n \le m \le 100 \\ 1 \le b \le r \\ 1 \le d \le r \\ 1 \le r \le 1000 \\ 1 \le a \le 1000 \\ 1 \le c \le 1000$

There will be a solution. Your result must be accurate to within ±10−6 absolute error, or ±10−6 relative error.

## 입력

On the first line will be the number of functions to solve, between 1 and 100 inclusive. Following that will be one line per function, giving the integer parameters separated by spaces in the order $$n$$, $$m$$, $$a$$, $$b$$, $$c$$, $$d$$, $$r$$.

## 출력

The value of the $$z \left[n/m \right]$$ should be printed in floating point format, one line per parameter set.

## 예제 입력 1

3
1 1 1 1 1 1 1
2 3 1 2 3 4 10
2 3 5 6 7 8 9


## 예제 출력 1

-1
0.4225806452
4.111111111