RearrangeAndMultiple

Sometimes it is possible to rearrange the digits of a positive integer to get a different positive integer that is a multiple of the original number. For example, the number x = 142857 does have this property if we use base 10. In base 10 we can rearrange the digits of x to get the number 285714, and we have 285714 = 2 * 142857.

(Note that adding leading zeros to the original number is not allowed. For example, it is not allowed to write the number 7 as 007 and then to rearrange those digits to get 700.)

You are given the ints L and b. Your task is to construct a positive integer x with the following properties:

• When written in base b, the integer x has exactly L digits.
• We can rearrange the base-b digits of x to get a different L-digit number that is a multiple of x.

If there is no such number, return an empty String. Otherwise, return a String that encodes the integer x as explained below. If there are multiple solutions, you may return any of them.

In order to return a positive integer x, do the following:

1. Take each of its base-b digits separately.
2. Write the value of that digit in base 10.
3. Return a String that contains all those values separated by single spaces.

For example, if b is 10 and x is 142857, you should return "1 4 2 8 5 7". Another example: if b is 16 and x is 2A0F (when written in base 16), you should return "2 10 0 15".