## Directi Interview Question for Software Developers

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AnswersYou are walking down the escalator to catch a subway train. The escalator itself moves at a speed of Ve meters per minute. You can walk down the escalator at a relative speed of Vy meters per minute. The length of the escalator is L meters. Trains arrive T minutes apart. Let t be the time between your arrival to the station if you stand still on the escalator and the arrival of the last train before your arrival. Assume that t is a random variable uniformly distributed between 0 and T. Return the probability of catching an earlier train if you choose to walk down the escalator instead of standing still on it.

- praveensinghraghav96 July 02, 2017 in India

Input :

The first line of the input contains an integer Tc denoting the number of test cases. Each test case contains the following 4 lines

Ve - velocity of escalator

Vy - your relative velocity with the escalator

L - length of escalator

T - Time Period of Trains

Output

For each test case, output a single line containing the expected probability having an absolute or relative error less than 10^-6.

Constraints

0 ≤ Tc ≤ 5 * 10 ^ 7

1 ≤ Ve ≤ 1000

1 ≤ Vy ≤ 1000

1 ≤ L ≤ 10 ^ 5

1 ≤ T ≤ 10 ^ 6

Example

Input:

2

10

10

20

2

10

10

100

4

Output:

0.5

1.0

Explanation

Example case 1. If you stand still, it'll take you 20/10 = 2 minutes to reach the bottom of the escalator. If you choose to walk, it'll make you 20/(10+10) = 1 minute. In the second case you save 1 minute and in 50% of the cases it'll allow you to catch an earlier train.

Example Case 2. Here, if you choose to walk instead of stand still, you will save 5 minutes and you will certainly be guaranteed to catch an earlier train.| Report Duplicate | Flag | PURGE

Directi Software Developer

**Country:**India

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