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.