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:
from math import sqrt
 
def largest_volume(p, s):
    sqrt_delta = sqrt(4*p*p-12*s)
    L = [(2*p+sqrt_delta)/6, (2*p-sqrt_delta)/6]
    H = [(p-2*L[0]),      (p-2*L[1])]
    V = [L[0]*L[0]*H[0],     L[1]*L[1]*H[1]]
    return max(V)
 
t = int(raw_input())
for i in range(t):
    p, s = map(int, raw_input().split())
    print '%0.2f' % largest_volume(p/4, s/2)