Largest inscribed rectangle

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Time limit2sMemory limit256 MB

Summary

Given radius R and bound B, find the largest area of a rectangle inscribed in the circle whose shorter side is at most B.

Level: Easy3 of 10
Topics: Math, Geometry
Solved: No attempts yet

Problem

A rectangle is inscribed in a circle of radius $R$ when all four of its corners lie on the circle. Find the largest area of an inscribed rectangle whose shorter side is at most $B$ . A square counts as a rectangle.

Input

The first line contains an integer $T$ , the number of test cases ( $1 \le T \le 1000$ ). Each of the next $T$ lines contains two integers $R$ and $B$ separated by a space ( $1 \le R, B \le 10000$ ).

Output

For each test case print the maximum area on its own line, rounded to three digits after the decimal point. Always print exactly three digits after the decimal point.

Examples2

Example 1
Input
```
3
1 1
1 2
2 2
```
Expected output
```
1.732
2.000
6.928
```

Example 2

Input

Expected output