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:
import math
t=int(raw_input())
while t>0:
    t-=1
    w=raw_input().split()
    p=float(w[0])
    s=float(w[1])
    b1=(p+math.sqrt((p**2) - (24*s)))/12
    b2=(p-math.sqrt((p**2) - (24*s)))/12
    x1=((2*b1*s)+(4*math.pow(b1,3))-(p*b1**2))/4
    x2=((2*b2*s)+(4*math.pow(b2,3))-(p*b2**2))/4
    print '%.2f'%(max(x1,x2))