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:
# Solution to "The Best Box" for CodeChef
# by Peter Mattsson (quantum.caffeine@gmail.com)

import sys
from math import sqrt

def read(inFile):
    t = int(inFile.readline())
    for _ in xrange(t):
        yield [int(x) for x in inFile.readline().split()]

def write(outFile, answer):
    outFile.write("%.2f\n"%answer)

def solve(p, s):
    a = (p - sqrt(p**2 - 24*s))/12.0
    return a**3 - (p*a**2)/4 + (s*a)/2

for case in read(sys.stdin):
    write(sys.stdout, solve(*case))