CTRICK  Card Trick
The magician shuffles a small pack of cards, holds it face down and performs the following procedure:
 The top card is moved to the bottom of the pack. The new top card is dealt face up onto the table. It is the Ace of Spades.
 Two cards are moved one at a time from the top to the bottom. The next card is dealt face up onto the table. It is the Two of Spades.
 Three cards are moved one at a time…
 This goes on until the nth and last card turns out to be the n of Spades.
This impressive trick works if the magician knows how to arrange the cards beforehand (and knows how to give a false shuffle). Your program has to determine the initial order of the cards for a given number of cards, 1 ≤ n ≤ 20000.
Input
On the first line of the input is a single positive integer, telling the number of test cases to follow. Each case consists of one line containing the integer n.
Output
For each test case, output a line with the correct permutation of the values 1 to n, space separated. The first number showing the top card of the pack, etc…
Example
Input: 2 4 5 Output: 2 1 4 3 3 1 4 5 2
hide comments
hardik agrawal:
20160322 03:58:39
wonder how!! but got AC in 1.74 using n^2 solution..


GAURAV CHANDEL:
20160125 11:10:50
You Beauty  BIT... 

A@$H!K:
20151008 10:14:52
My first proper BIT! :D 

bicsi:
20150830 15:57:22
0.98s with a cyclic list. FAIL 

S@nKeT:
20150826 13:25:55
Last edit: 20150826 13:27:59 

sHaShAnK sHeKhAr:
20150723 10:22:51
How can we prove that such configuration of cards will always exist for all values of n??


rini22:
20150710 09:15:31
Last edit: 20160731 16:21:52 

i_am_looser:
20150529 20:55:02
segment Trees.... ; ) 

Basant kumar bhala:
20150301 08:31:14
1.39s with linked lists 

mkrjn99:
20150126 06:19:59
nlog^2(n) :D 
Added by:  Camilo Andrés Varela León 
Date:  20061123 
Time limit:  3.279s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL JSRHINO NODEJS PERL6 VB.NET 
Resource:  Nordic Collegiate Contest 2006 