Kata

Lexicographic permutations are ordered combinations of a set of items ordered in a specific way.

For instance, the first 8 permutations of the digits 0123, in lexicographic order, are:

1st 0123
2nd 0132
3rd 0213
4th 0231
5th 0312
6th 0321
7th 1023
8th 1032

Your task is to write a function L( n, d ) that will return a string representing the nth permutation of the d digit, starting with 0 (i.e. d=10 means all digits 0123456789).

So for d = 4, L(7,4) should return '1023', and L(4,4) should return '0231' .

Some things to bear in mind:

• The function should return a string, otherwise permutations beginning with a 0 will have it removed.

• Test cases will not exceed the highest possible valid values for n

• The function should work for any d between 1 and 10.

• A value of 1 for n means the 1st permutation, so n = 0 is not a valid input.

• Oh, and no itertools ;)