cp/daily/305easy

[2017-03-06] Challenge #305 [Easy] Permutation base

There may be an actual name to this base system (let us/me know in comments), and there is a math insight that makes this problem even easier, but it is still pretty easy with no math insight.

For permutation base 2, the indexes and values start with:

index	value
0	0
1	1
2	00
3	01
4	10
5	11
6	000
7	001
8	010
9	011

Sample challenge

What is the base-value for index 54?

What is the index-value for base 111000111?

Example

permbase2 54
1 1 0 0 0

permbase2 inv 1 1 1 0 0 0 1 1 1
965

Challenge index inputs (some are 64-bit+ inputs)

234234234
234234234234234
234234234234234234234234

Challenge value inputs

000111000111111000111111000111111000111
11111111000111000111111000111111000111111000111

Bonus

Extend the function to work with any base. Base 10 index value 10 is 00. Index value 109 is 99