Find the permutation by its number in lexicographic order.
Input
The first line of the input contains the number N (1 <= N <= 12) – the number of elements in the permutation, in the second – number K (1 <= K <= N!) – permutation number.
Imprint
Print N numbers – desired permutation.
Examples
| # |
Input |
Output |
| 1 |
3
2 |
1 3 2 |