Problem: Johnny needs to make a rectangular box for his physics class project. He has bought P cm of wire and S cm^2 of special paper. He would like to use all the wire (for the 12 edges) and paper (for the 6 sides) to make the box.
What is the largest volume of the box that Johnny can make?

Input
The first line contains t, the number of test cases (about 10). Then t test cases follow.

Each test case contains two integers P and S in a line (1 ≤ P ≤ 40000, 1 ≤ S ≤ 20000). You may assume that there always exists an optimal solution for the given input cases.


Output
For each test case, print a real number that is the largest volume of the box that Johnny can make, rounded to two decimal places.

Example

Input:
2
20 14
20 16

Output:
3.00
4.15

Output details
First case: the dimensions of the largest box may be 3, 1 and 1.
Second case: the dimensions of the largest box may be 7/3, 4/3 and 4/3.

Solution (in PYTHON):

Solution:
for _ in xrange(input()):
    p, s = map(int, raw_input().split())
    l1 = (p + (p ** 2 - (4 * 6 * s)) ** 0.5) / (2 * 6)
    l2 = (p - (p ** 2 - (4 * 6 * s)) ** 0.5) / (2 * 6)
    v1 = round(l1 * l1 * (p/4 - (2 * l1)), 2)
    v2 = round(l2 * l2 * (p/4 - (2 * l2)), 2)
    print v1 if v1 > v2 else v2