As a world-famous traveler, Prof. Pang's research interest is to travel as many places as possible in his life.

We have a segment . There are two travelers on it. The first one is on position with velocity (which means s/he can walk unit on the segment per second). The second one is on position with velocity .

From their respective beginning points, travelers can walk on the segment. They cannot walk outside the segment. Whenever they want to change their direction, they can turn around immediately.

Please help Prof. Pang to calculate the minimum possible time by which every position of the segment is passed by at least one traveler.

The first line contains one integer  -- the number of test cases.

The i-th of the next test lines contains five numbers  (, , ). All numbers have at most 3 digits after the decimal point.

For each test case, we should output one number -- the minimum time that every position of the segment is passed by at least one traveler.

Your answer is considered correct if its absolute or relative error does not exceed .

2
10000.0 1.0 0.001 9999.0 0.001
4306.063 4079.874 0.607 1033.423 0.847

5001000.0000000000
3827.8370013755