Two Snails

Vasya sat by a window and noticed two snails on a pole, crawling upward. Vasya began watching them. He noticed that in one hour the first snail climbs $a_1$ centimeters and the second snail climbs $a_2$ centimeters.

The next morning Vasya noticed that the snails were lower than they had been in the evening. He realized that during the night the first snail slides down $b_1$ centimeters per hour and the second snail slides down $b_2$ centimeters per hour.

$z$ hours passed since the start of the observation, and Vasya wondered: during what period of time was the first snail higher than the second over these $z$ hours?

Vasya decided to assume that the snails move at their respective constant speeds both day and night, and that day and night each last 12 hours. The observation started at the beginning of the day, when the snails were at the same height. The height of the pole and the initial positions of the snails are such that the snails never leave the bounds of the pole.

The first line contains a positive integer $t$ ($1 \le t \le 10^4$), the number of test cases in the input. The descriptions of the test cases follow.

Each test case contains five positive integers $a_1$, $b_1$, $a_2$, $b_2$, and $z$ ($1 \le a_1, b_1, a_2, b_2 \le 100$, $1 \le z \le 10^5$), the speeds of the snails and the time period Vasya is interested in.

The sum of $z$ over all test cases is guaranteed not to exceed $10^6$.

Output $t$ lines. For each test case, output a single real number $x$, the time during which the first snail was higher than the second. Print each number on its own line. All numbers must be printed with an absolute or relative error of at most $10^{-6}$.

Note that printing long double values in C++ does not work correctly in the compiler version used by the judges. We apologize and will try to fix this as soon as possible, but for now we recommend using the double type.