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=input()
while(t>0):
	p,s=map(int,raw_input().strip().split())
	p1,s1=p/4,s/2
	z1=(p1+math.sqrt(p1*p1-3*s1))/3
	z2=(p1-math.sqrt(p1*p1-3*s1))/3
	res=max((z1**3-p1*z1*z1+s1*z1),(z2**3-p1*z2*z2+s1*z2))
	print round(res,2)
	t-=1