UCV2013I  Tambourine
Little HH loves tambourines. He loves them so much that now he wants to build them. A tambourine is a musical instrument shown in Figure 1(a). As you can see in Figure 1(b) the tambourine is just a big circle of radius R with N smaller circles of radius r (r < R).
Figure 2: (a) A tambourine. (b) The radius of the circles is shown. (c) There is a 2N sides regular polygon inscribed in the outter circle
HH knows the radius of the small circles (r), he also knows the number of small circles that he has (N). And he knows that the small circles should be centered on the center of the even sides of a 2N sides regular polygon inscribed in the big circle (the sides of this polygon each measuring 2r), as shown on Figure 1(c). Now HH wants you to help him find the radius R of the big circle.
Input
The input contains several test cases. Each test case consists of two values r and N as described previously. (0 < r <= 100), (2 <= N <= 10000).
The end of input is indicated by a test case with r = N = 0.
Output
For each test case you must print a number (rounded up to two decimal places) showing the radius of the big circle to build the tambourine.
Example
Input: 1 4
2 4
1 8
0 0 Output: 2.61
5.23
5.13
hide comments
bayulaxana:
20180118 09:29:22
Use double instead of float. As many others said, take care the value of Phi.


mishra_sharad:
20160825 12:30:19
50th...in one go...just be careful about value of pi n take float... 

sriraj:
20160811 02:04:09
Using M_PI in C++ is a must 

ajay_5097:
20160410 23:45:26
that was the easy one AC in 1 go :) 

queen_123:
20160122 12:42:23
python...rocks 

shubham_174:
20150814 22:32:12
AC in 1st go..... :p


sy_117:
20150814 21:51:51
Using pi=3.145926 & cosine formula give me 2 WA...So plz ...SINE Formula@@@@


Jaswanth:
20150813 17:49:44
use M_PI (c++ math.h) rest of PI values give WA 

kartikay singh:
20150526 12:27:49
use double


anksin:
20150520 00:09:08
Use math.h M_PI for pi constant.......easy trigonometry.....any side of the polygon will subtend an angle at the center, and using Right Angle Triangle we can easily find the radius!!! 
Added by:  Hector Navarro 
Date:  20130722 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 
Resource:  Local UCV 2013. Héctor Navarro 