Max and Cards

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Points: 7 (partial)
Time limit: 1.0s
Memory limit: 64M

Authors:
Problem type

Max is a magician whose job is to shuffle magic cards and confuse innocent bystanders. He uses a special deck with N cards, labelled from 1 to N. Suddenly, he throws his hands up in the air and the cards fall back down in sorted order (from least to greatest). He then quickly swipes his hands over the cards and forms all N! possible permutations from lexicographically least to greatest ordered from 0 to N!-1. For example, if N=3 then he would have made the permutations

1 2 3
1 3 2
2 1 3
2 3 1
3 1 2
3 2 1

Afterwards, Max asks you Q questions in the form of what was the Q_i^{th} permutation that Max made. Since your tiny eyes were too slow to see Max's amazing trick, you try using your old Pentium 4 computer to recreate Max's magic, but can you do it fast enough?

Input

The first line will contain N (3 \le N \le 19).
The second line will contain Q (3 \le Q \le 100).
The next Q lines will contain Q_i (0 \le Q_i < N!).

Output

For each question, output the Q_i^{th} permutation on its own line.

Scoring

At least 50% of the test cases will have N \le 10.

Sample Input

3
6
5
4
3
2
1
0

Sample Output

3 2 1
3 1 2
2 3 1
2 1 3
1 3 2
1 2 3

Comments


  • 2
    HowAboutNo  commented on Jan. 10, 2016, 4:55 p.m.

    Judge down right now and I have a solution for partial marks. What do?


    • 3
      Xyene  commented on Jan. 10, 2016, 5:03 p.m.

      A judge has been made available.


      • 2
        HowAboutNo  commented on Jan. 10, 2016, 5:39 p.m. edited

        Thanks! Couldn't implement the problem well enough, but extra points are extra points.

        Edit: The points are partial, but they aren't showing up under my score.


        • 3
          bobhob314  commented on Jan. 10, 2016, 5:48 p.m.

          Pretty sure it's fixed now.


      • 4
        bobhob314  commented on Jan. 10, 2016, 5:06 p.m.

        Could you give him an extra submission? I think his timer ran out before he could submit for partial.