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
trials = int(raw_input())
for i in xrange(trials):
    p, s = map(int,raw_input().split())
    ya0 = p/4
    ya1 = -2
    b=4*ya0
    a=-6
    c=-s
    x_0 = (-b+math.sqrt(math.pow(b,2)-4*a*c))/(2*a)
    x_1 = (-b-math.sqrt(math.pow(b,2)-4*a*c))/(2*a)
    y_0 = ya0+ya1*x_0
    y_1 = ya0+ya1*x_1
    print("%.2f" % max(x_0*x_0*y_0, x_1*x_1*y_1))