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#### Source file: kthperm.cc

You are to write a program that has to generate particular permutations
of the first N nonegative integegers. Consider all of the permutations
of the integers { 0, 1, 2, ..., N } to be ordered lexicographically, i.e.,
the order they would appear in a dictionary if 0 == a, 1 == b, 2
== c, and so on. Thus, under this ordering and indexed from zero,
the six permutations of the sequence { 0, 1, 2 } are

zeroth: { 0, 1, 2 }

first: { 0, 2, 1 }

second: { 1, 0, 2 }

third: {1, 2, 0 }

fourth: { 2, 0, 1 }

fifth: { 2, 1, 0 }

##
Input

The input file consists of several pairs of nonnegative integers. The first,
**K**, will be between 0 and 2^32-1 (a value that will fit in an *unsigned
long*); the second, **N**, will be between 1 and 13, inclusive. It
will always be the case that **K** is less than ** N**! .
##
Output

For each line in the input file, the output file should print the **K**th
permutation (under the lexicographic ordering above) of the sequence `{
0, 1, ..., `**N**-1 }. The sequence should be printed with a single
space between each pair of integers and with no trailing spaces.
##
Sample
Input

5 3
0 12
10 10
1000000000 13

##
Sample
Output

2 1 0
0 1 2 3 4 5 6 7 8 9 10 11 12
0 1 2 3 4 5 7 9 6 8
2 1 0 8 10 7 9 12 4 6 11 3 5