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
omar_hafez:
20220516 00:08:05
HINT:


pravesh_pandey:
20220413 08:18:59
Will someone correct me if I'm wrong, I think the time complexity will be N*log(N)*log(N) if I have done with the BIT method. 

madhav10:
20210512 17:42:51
@r15habhgup11


princemishra:
20210408 09:57:59
input:


karelisp:
20210330 01:12:42
Take care of testcase where N=1 

sharjeel_spoj:
20210125 22:20:21
Segment tree can be used to find the Kth largest element. 

sangmai:
20210118 14:09:16
bruteforce passes. 

anirudh_1999:
20200506 21:15:02
Can anyone explain the sample test cases given in the problem..I couldn't understand any of it. 

jwalinarora:
20200418 17:19:46
There can be multiple answers, right? 

atharvat77:
20191119 20:11:18
BIT On Point Nice Problem 
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 