oval-and-rectangle

Problem Description

Patrick Star find an oval. The half of longer axes is on the x-axis with length $a$. The half of shorter axes is on the y-axis with length $b$. Patrick Star plan to choose a real number $c$ randomly from $[0, b]$, after that, Patrick Star will get a rectangle :

1. The four vertexes of it are on the outline of the oval.
2. The two sides of it parallel to coordinate axis.
3. One of its side is $y = c$. Patrick Star want to know the expectations of the rectangle's perimeter.

Input

The first line contain a integer $T$ (no morn than 10), the following is $T$ test case, for each test case : Each line contains contains two integer a, b ($0 < b < a < 10^5$). Separated by an white space.

Output

For each test case output one line denotes the expectations of the rectangle's perimeter . You should keep exactly 6 decimal digits and ignore the remain decimal digits. It is guaranted that the 7-th decimal digit of answer wont be 0 or 9.

Sample Input

1

2 1

Sample Output

8.283185

Source

2018 Multi-University Training Contest 6