{-# LANGUAGE OverloadedStrings #-}

import qualified Data.ByteString.Lazy.Char8 as C
import Data.Char (isDigit, digitToInt)

-- | Generates as many digits of pi.
-- Based on <http://www.cs.ox.ac.uk/people/jeremy.gibbons/publications/spigot.pdf this article> .
pi_ :: Integral a => [a]
pi_ = g (1, 0, 1, 1, 3, 3) where
    g (q, r, t, k, n, l)
        | 4 * q + r - t < n * t = n : g (10 * q, 10 * (r - n * t), t, k, div (10 * (3 * q + r)) t - 10 * n, l)
        | otherwise = g (q * k, (2 * q + r) * l, t * l, k + 1, div (q * (7 * k + 2) + r * l) (t * l), l + 2)

correct :: C.ByteString -> [Int]
correct = correct_ pi_
correct_ ps ss
    | (not . isDigit) hs = correct_ ps ts
    | digitToInt hs == hp = correct_ tp ts
    | otherwise = [digitToInt hs, hp]
    where
        hp = head ps
        hs = C.head ss
        tp = tail ps
        ts = C.tail ss

main :: IO ()
main = putStrLn . unwords . map show . correct =<< C.getContents