Problems
Permutation by number
Permutation by number
Find a permutation by its number in the lexicographical order.
\InputFile
The first line of the input file is written the number \textbf{N} (\textbf{1} ≤ \textbf{N} ≤ \textbf{12}) - the number of elements in the permutation.
In the second row the number of \textbf{K} (\textbf{1} ≤ \textbf{K} ≤ \textbf{N!}) - number of the permutation.
\OutputFile
The output file output of \textbf{N} numbers - the desired permutation.
Input example #1
3 1
Output example #1
1 2 3