Kindergarten Physics

Problem Description

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

Source

2020 Multi-University Training Contest 4