Convert Base 10 to Base 1.1 Million

Base10M

module Base10M
(encode
,decode) where

import Data.List(elemIndex)
import Data.Maybe(fromJust)

unicodes = ['a'..]
numOfUnicodes = toInteger $ length unicodes

numToDigs :: Integer -> Integer -> [Integer]
numToDigs 0 _ = []
numToDigs x b = numToDigs (x `div` b) b ++ [x `mod` b]

digsToNum :: [Integer] -> Integer
digsToNum [] = 0
digsToNum (x:xs) = x * (numOfUnicodes ^ (length xs)) + digsToNum xs

numToUni :: Integer -> Char
numToUni x = unicodes !! fromInteger x 

uniToNum :: Char -> Integer
uniToNum x = toInteger $ fromJust $ elemIndex x unicodes

encode :: Integer -> [Char]
encode x = map numToUni $ numToDigs x numOfUnicodes

decode :: [Char] -> Integer
decode x = digsToNum $ map uniToNum x