--
-- addition of very long integers
--

import Data.Char
import Data.String

addRev [] [] 0 = []
addRev la [] c = addRev la [0] c
addRev [] lb c = addRev [0] lb c
addRev (a:la) (b:lb) c = q : (addRev la lb p) where (p,q) = divMod (a+b+c) 10

add la lb = reverse (addRev (reverse la) (reverse lb) 0)

stringToDigits s = map digitToInt s
digitsToString l = map intToDigit l
intToDigits n = map digitToInt (show n)
digitsToInt :: [Int] -> Integer
digitsToInt s = read (digitsToString s)

verifyAdd m n = ((digitsToInt (add (intToDigits m) (intToDigits n))) - (m+n)) == 0

main = do print (digitsToString (add (stringToDigits "67544539703981792301876431982341329878656543656") (stringToDigits "923409765450275928347539864398234659")))
          print (all (id) [verifyAdd x y | x <- [12000..13000], y <- [7500..8500]])