Migrated from Lutece 667 Cookiezi's perfect OSU class

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Description

OSU is a music game.

Cookiezi is an OSU player.There're $N$ beatmaps in his computer.

There're so many beatmaps that Cookiezi doesn't want to play them all within today.So he decides to choose $X$ beatmaps.

He comes up with an idea to choose those beatmaps.

1. Put all beatmaps into sequence One and number them from $1$ to $N$;
2. Get out those beatmaps which are in odd position of the sequence One to form a new sequence Two;
3. Let the remaining beatmaps to form a new sequence Three;
4. Add the sequence Two to the tail of the sequence Three to form a new sequence One.
5. repeat step $2\sim 4$ for $M-1$ times.

After all steps above,he chooses the first $X$ beatmaps to play.

Now ,$N,M,X$ are given.Cookiezi wants you to tell him what beatmaps he will choose.

Notice:the first position of a sequence is numbered $1$,the second is $2$,and so on.

Input

In the first line there's a integer $T$($T\leq 200$) means the number of cases.

In the next $T$ lines there're $3$ integer $N,M,X$($N\leq 1000000$, $M\leq 20$, $X\leq 20$, $X\leq N$)

Output

For every case,you should output $X$ numbers,representing the beatmaps Cookiezi will choose. A space must be output between every two numbers.There shouldn't be any other space at the end of each line.

Samples

3
5 1 2
5 2 2
4 3 3

2 4
4 3
3 1 4

Note

In the third sample.

• After $0$ times : 1 2 3 4
• After $1$ times : 2 4 1 3
• After $2$ times : 4 3 2 1
• After $3$ times : 3 1 4 2

So print 3 1 4

Resources

135678942570