Small GCD Sort Practice Coding Problem

Difficulty:1039

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Small GCD Sort

There are $N$ players, numbered from $1$ to $N$ .

Player $i$ 's score is defined to be $\gcd(i, N)$ .
Here, $\gcd(i, N)$ refers to the largest positive integer that divides both $i$ and $N$ .

Your task is to find an ordering of the players, from left to right, that satisfies the following conditions:

Between two players with different scores, the one with a higher score must appear somewhere to the left of the one with a lower score.
Between two players with the same score, the player with a smaller number must appear somewhere to the left of the one with a lower score.

It can be proved that these rules uniquely define an ordering of the $N$ people.
Your task is to find this ordering.

Input Format

The first line contains a single integer $T$ — the number of test cases.
Each of the next $T$ lines contains a single integer $N$ — the number of players.

Output Format

For each test case, print $N$ space-separated integers on a new line — the player numbers in the required preference order.

Constraints

$1 \leq T \leq 100$
$1 \leq N \leq 100$

Sample 1:

Input

Output

Explanation:

Test case $1$ : There is only one player.

Test case $2$ : There are two players.
Player $1$ has a score of $\gcd(1, 2) = 1$ , while player $2$ has a score of $\gcd(2, 2) = 2$ .
Player $2$ has a higher score, and so appears to the left of player $1$ , making the only possible order $[2, 1]$ .

Test case $4$ : There are four players. It can be verified that players $1$ and $3$ have a score of $1$ , player $2$ has a score of $2$ , and player $4$ has a score of $4$ .
So,

Player $4$ has the highest score, and so must be placed first.
Player $2$ has the second highest score, and so must be placed second.
Players $1$ and $3$ have the same score.
Among them, $1$ has the smaller number, and so must be placed ahead of $3$ .

Thus, the final order is $[4, 2, 1, 3]$ .

More Info

Time limit1 secs

Memory limit1.5 GB

Source Limit50000 Bytes

Author(s)

archit_adm

Tester(s)

kingmessi

Editorialist(s)

iceknight1093

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                                        #include
                                          <bits/stdc++.h>
                                      
                                        using
                                        namespace
                                        std;
                                      
                                        int
                                        main()
                                        {
                                      
                                        // your code goes here
                                      
                                        }
                                      
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