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())
for _ in xrange(t):
	p,s = map(float, raw_input().split())
	val  = math.sqrt((p*p)-(24*s))
	l1 = (p + val)/12.0
	l2 = (p -val)/12.0
	if l1 <0:
		ans = l2
		print "%.2f" %ans*ans*((p/4.0)-(2*ans))
	elif l2<0:
		ans =l1
		print "%.2f" %ans*ans*((p/4.0)-(2*ans))
	else:
		print "%.2f" %max(l1*l1*((p/4.0)-(2*l1)), l2*l2*((p/4.0)-(2*l2)))