HDU6812 Kindergarten Physics（假物理题真思维）

Zhang3 a participant of IPhO (Immortal Physics Olympiad). The $0^\mathrm{th}$ problem in the contest is as follows.

There are two balls that weigh $a$ kg and $b$ kg respectively. They can be regarded as particles in this problem, as they are small enough. At the very beginning (i.e. $t = 0$), the distance between two balls is $d$ km, and both of them are not moving.

Assuming that only gravitation works in this system (no other objects or other forces considered). The two balls has started moving since $t = 0$. Your task is to calculate the distance between them when $t = t_0$ (s).

Help Zhang3 solve the problem!

The following information might help when solving the problem.

- Universal gravitation formula: $F = G \cdot m_1 \cdot m_2 / r ^ 2$

- Gravitational constant: $G = 6.67430 \times 10^{-11} \; \mathrm{m}^3 / (\mathrm{kg} \cdot \mathrm{s}^2)$

Input

The first line of the input gives the number of test cases $T \; (1 \le T \le 100)$. $T$ test cases follow.

For each test case, the only line contains four integers $a, b, d, t_0 \; (1 \le a, b, d, t_0 \le 100)$, representing the mass of the two balls, the initial distance between them, and how much time the balls move.

It is guaranteed that two balls will not collide within $(t_0 + 1)$ seconds.

Output

For each test case, print a line with a real number $x$, representing that the distance is $x$ km.

Your answers should have absolute or relative errors of at most $10^{-6}$.

Sample Input

3
1 2 3 4
7 73 7 68
100 100 1 100

Sample Output

2.99999999999999999982
6.99999999999999974807
0.99999999999993325700

显然，两个质点移动的距离与质量、时间正相关，与距离负相关。自己估算或者观察样例，发现在 数据范围可能的最坏情况下 $a=b=t_0=100,d=1$，质点移动的距离远小于 $10^{-6}$（所容许的误差值）， 所以对于任意数据范围内的输入，都直接输出 d 即可。

哭了.