0122. Generation of a Permutation

Input file name:	gen.in
Output file name:	gen.out
Time limit:	500 ms
Memory limit:	64 megabytes

Generate a permutation of 1 ≤ N ≤ 100 elements by its lexicographical number 1 ≤ K ≤ N!.

Input file

The only line of input contains N and K separated by an arbitrary number of whitespace characters.

Output file

In the only line of output file print N different integers x₁,…,x_N ranging from one to N, separated by single spaces. No trailing spaces are allowed.

Examples:

gen.in	gen.out
3 2	1 3 2

Source: Petrozavodsk Summer 2003. Blitz Kontest, Monday, August 25
Author: Andrew Lopatin, Nick Durov

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