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
abhinav_jain02:
20190523 20:06:18
Great concept


udayps055:
20190522 00:36:34
can anyone explain the test case how it varies in 4 and 5 

knir0103:
20190407 07:04:45
cost me 2 days because of mod operator in the circle, Ac finally! 

rsazid77:
20171212 09:59:18
i think this a very good problem if you use treap, then it will be easier to implement :) 

holmesherlock:
20170519 13:38:59
easy on paper,,implementation was slightly tough 

sas1905:
20170511 12:42:24
n=1 ans=1 got 1 WA for this..But undoubtedly one of the best problems on BIT..!! 

tsioftas:
20170422 08:54:35
The constraints of n are wrong, it gets bigger than 20000. It costed me a wa (not a sigsev somehow xD) 

avisheksanvas:
20170202 12:22:19
BIT to the rescue _/\_ 

Rakend Chauhan:
20170104 18:20:21
easy one with vector 

king:
20161218 13:01:47
Bit + binary search = AC ;)

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 