[r]

When Jordi and Mireia married several years ago,
they put their gold together to buy a circular field
with a radius of 1000 meters.
Jordi put *J* kg of gold, and Mireia put *M* kg.
Time has passed and they divorce,
so they have decided to divide the field
in such a way that each one receives an area
proportional to the gold invested by he or she.
They will use a rope of length *L* meters,
tie one extreme to the easternmost point,
and use the other extreme to mark the limit of the fields.
Since Jordi is a gentleman,
he will settle for the left, worst shaped field,
while Mireia will get the field to the right,
painted green in the picture.

The problem you must solve is:
given the amounts of gold *J* and *M*,
which must be the length *L* of the rope?

**Input**

Input begins with the number of cases.
Every case consists of two real numbers
*J* ∈ [1, 100] and *M* ∈ [1, 100].

**Output**

For every case, print the length *L* of the rope
with four digits after the decimal point.
The input cases have no precision issues.

Public test cases

**Input**

2 1 20 10 6.420421

**Output**

1849.2414 1000.0000

Information

- Author
- Salvador Roura
- Language
- English
- Official solutions
- C++
- User solutions
- C++
- Event
- Tercer Concurs de Programació de la UPC - Final
- Date
- 2005-09-28