largest-volume-84_36822
Now our heroes - Maga and Alex are working for Oil Company as developers. Recently they have faced a great problem. 

They couldn’t find the correct solution. Could you help them?

We are given r – radius of lower base and s – slant height. The figure can be cylinder or truncated cone. You have to find as largest volume as possible to carry oil respect to given information. The slant height is the shortest possible distance between the edges of two bases through surface of cone.

  

Input :

You are given 2 numbers. r– radius of lower base and s – slant height.

Output:

Largest Volume. Print 2 digits after floating point.

Constraints:

1 ≤ r, s ≤ 100

SAMPLE INPUT
1 1

SAMPLE OUTPUT
4.33

Explanation

In the sample test case, the answer is that it is truncated cone which the area of upper base is larger than the area of lower base. And then answer is simple 4.33.
import math
r,s=map(int,raw_input().split())
max_V=0
R=r
h=s
while h>=0:
	t=s**2-(R-r)**2
	if t<0:
		break
	h=t**.5
	V=(math.pi*h)*(r**2+R**2+R*r)/3.0
	if V>=max_V:
		max_V=V
	R=R+0.001
	
print"%0.2f" % max_V
1 1

SAMPLE 97 33 68 95 78 99 97 21 54 95 78 70 1 2

SAMPLE 184 21 54 181 54 70 2 2

SAMPLE 184 0 54 91 54 112 0 2

SAMPLE 54 135 54 22 -1 2

SAMPLE 54 5 54 18 -2 2

SAMPLE 57 5 17 18 108 1 50 5 17 26 142 1 50 10 17 30 0 1

S@NPLE 50 6 16 30 21 6 30 30 1 1

S@NPLD 30 29 2 1

S@NPLD 54 29 3 1

S@NPLD 54 47 36 47 64 1 1 3 36 56 124 1 24 56 94 1 0 3 24 87 71 1 24 158 -1 1

E@PNMR 24 268 -2 1

E@PNMR 25 268 25 106 25 41 43 41 0 4 9 41 1 4 8 41 2 4 8 3 3 3 3 6 11 1 -1 7 -1 3 0 5 1 7 1 8 1 15 2 15 3 15 3 21 6 21 4 21 0 21 1 21 2 21 4 1

@EMORO 5 21 10 21 10 37 3 2

?EMORO 14 37 2 37 0 37 0 41 0 15 0 26 -1 26 -1 14 0 40 0 65 1 65 -1 65 -1 120 -1 235 0 235 0 407 0 20
4.33 1028727.30 2291771.52 2959896.28 634924.24
 1706898.12
 1759980.78
 13.71
 2248036.15
 6168918.71
 1015894.52
 34.66
 0.00
 1581107.70
 2312487.39
 3.22
 3331378.80
 217000.17
 6.28
 45999.80
 173558.62
 25.13
 51230.65
 23163.16
 36645.11
 39465.13
 41686.13
 63348.64
 80076.41
 53552.70
 0.40
 47460.40
 49836.90
 8637.81
 116977.07
 4.33
 111345.88
 13.97
 299581.01
 29.76
 559442.97
 304474.04
 12869.53
 30.85
 407522.58
 48306.70
 254924.71
 27760.68
 10.88
 643950.04
 15838.34
 2670405.19
 3.14
 10634151.43
 12.57
 10768314.90
 1039559.77
 149572.58
 321449.51
 25.80
 57352.02
 58.18
 53326.57
 109.70
 642.79
 116.98
 370.25
 381.70
 79.37
 9.42
 50.38
 225.65
 318.03
 1724.74
 2153.63
 2650.03
 6092.63
 9306.92
 7065.45
 3732.80
 4429.32
 5214.89
 51.78
 8136.05
 15036.57
 48766.30
 67.19
 64984.68
 24777.94
 20416.53
 27779.75
 1360.35
 7084.30
 6135.64
 843.72
 25796.26
 110692.14
 117082.41
 104567.14
 675417.40
 5149639.86
 5230946.98
 27174399.71
 3224.53
