ANARC08H  Musical Chairs
In an attempt to create a similar game on these days' game consoles, you modify the game in the following manner: N Children are seated on N chairs arranged around a circle. The chairs are numbered from 1 to N . Your program preselects a positive number D . The program starts going in circles counting the children starting with the first chair. Once the count reaches D , that child leaves the game, removing his/her chair. The program starts counting again, beginning with the next chair in the circle. The last child remaining in the circle is the winner.
For example, consider the game illustrated in the figure above for N = 5 and D = 3 . In the figure, the dot indicates where counting starts and × indicates the child leaving. Starting off, child #3 leaves the game, and counting restarts with child #4. Child #1 is the second child to leave and counting restart with child #2 resulting in child #5 leaving. Child #2 is the last to leave, and child #4 is the winner. Write a program to determine the winning child given both N and D .
Input
Your program will be tested on one or more test cases. Each test case specifies two positive integers N and D on a single line, separated by one or more spaces, where N, D < 1,000,000 .
The last line of the input file contains two 0's and is not part of the test cases.
Output
For each test case, write the winner using the following format:
N D W
Where N and D are as above, is a space character, and W is the winner of that game.
Example
Input: 5 3 7 4 0 0 Output: 5 3 4 7 4 2
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shubiks:
20160718 03:57:21
AC in one go. Thanks to comments! :D 

karthik1997:
20160611 10:16:30
Linked List approach fails => O(N * Log(base d)N ) approach gives TLE


galloska:
20150820 00:23:13
I solved it using BIT, but that's not the best option to solve it... In live archive you get TLE if you use BIT or Segment Tree.


shravinson:
20150717 09:31:00
can i use linked list to solve this problem??? 

[Mayank Pratap]:
20150607 17:23:05
Had a hard time understanding .....Finally AC :) 

Steven Hans Limantoro:
20150606 12:24:27
Hint : Josephus problem (iterative version)


farziengineer:
20150527 11:43:48
there was a question on spoj by the name anarch(maybe),[required some bitwise implementation.], but now i cant find that question on spoj, please help 

i_am_looser:
20150511 14:15:07
Solved using segment tree but it took 2 hours to implement .... 

Gaurav chandel:
20150228 12:13:35
@Ankit recursion will lead to stack overflow. Use iterative version :) 

Ankit Aggarwal :
20150118 17:55:32
why is recursive solution leads to SIGSERV?? 
Added by:  Ahmed Aly 
Date:  20090704 
Time limit:  13.93s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL JS NODEJS PERL 6 VB.net 
Resource:  ANARC 2008 