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:
a=input()
for i in range(a):
    p,s=map(int,raw_input().strip().split())
    p,s=[int(p),int(s)]
    p=p/4.0
    s=s/2.0
    l1=(2*p+(4*p*p-12*s)**0.5)/6.0
    l2=(2*p-(4*p*p-12*s)**0.5)/6.0
    if l1<p/3.0 and l1>0:
        l=l1
    elif l2<(p/3.0) and l2>0:
        l=l2
    v=s*l-(l*l*p) +(l*l*l)
    print str(round(v,2))