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:
t = input()

import math
i = 0
while i < t :
    p, s = map(int, raw_input().split())
    d = float(math.sqrt((p*p)- (24*s)))
    l = float(p +d)/12
    ld = float(p - d)/12
    h = float(p-(8*l))/4
    hd = float(p-(8*ld))/4
    if l*l*h > (ld*ld*hd) :
        print '%0.2f' % l*l*h
    else :
        print '%0.2f' % (ld*ld*hd)
    
    i = i+1