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CTRICK - Card Trick

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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

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	prasoonjha1: 2023-04-08 07:58:22 What is the meaning of "new top card is dealt with face up onto the table". Is it removed from the pack or what?
	newacc09_: 2023-01-10 22:13:16 a good way is simply to use sortedcontainers in python but you can't run it on (as they need to be downloaded as third party module) spoj so here is the code from sortedcontainers import SortedList for _ in range(int(input())): n = int(input()) res = [-1] * (n+1) p = 0 s = SortedList(list(range(1,1+n))) for i in range(1, n+1): x = (p + i) % len(s) res[s[x]] = i p = x s.remove(s[x]) print(*res[1:])
	omar_hafez: 2022-05-16 00:08:05 HINT: Try to find the pattern of things in this problem :)
	pravesh_pandey: 2022-04-13 08:18:59 Will someone correct me if I'm wrong, I think the time complexity will be Nlog(N)log(N) if I have done with the BIT method.
	madhav10: 2021-05-12 17:42:51 @r15habhgup11 thanks for the hint man.
	princemishra: 2021-04-08 09:57:59 input: 1 50 output: 41 1 45 39 2 9 17 15 3 25 24 36 26 4 23 19 13 43 10 5 47 46 27 22 30 44 6 48 33 34 16 28 11 21 7 18 14 42 32 50 40 35 38 8 37 29 20 12 31 49
	karelisp: 2021-03-30 01:12:42 Take care of testcase where N=1
	sharjeel_spoj: 2021-01-25 22:20:21 Segment tree can be used to find the Kth largest element.
	sangmai: 2021-01-18 14:09:16 bruteforce passes.
	anirudh_1999: 2020-05-06 21:15:02 Can anyone explain the sample test cases given in the problem..I couldn't understand any of it.

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Added by:	Camilo Andrés Varela León
Date:	2006-11-23
Time limit:	3.279s
Source limit:	50000B
Memory limit:	1536MB
Cluster:	Cube (Intel G860)
Languages:	All except: ERL JS-RHINO NODEJS PERL6 VB.NET
Resource:	Nordic Collegiate Contest 2006