Problem:
Score : 200 points

Problem Statement

You are given positive integers A and B.

Find the K-th largest positive integer that divides both A and B.

The input guarantees that there exists such a number.

Constraints

All values in input are integers.

1 \leq A, B \leq 100

The K-th largest positive integer that divides both A and B exists.

K \geq 1

Input

Input is given from Standard Input in the following format:

A B K

Output

Print the K-th largest positive integer that divides both A and B.

Sample Input 1

8 12 2

Sample Output 1

2

Three positive integers divides both 8 and 12: 1, 2 and 4.
Among them, the second largest is 2.

Sample Input 2

100 50 4

Sample Output 2

5

Sample Input 3

1 1 1

Sample Output 3

1

Solution in Haskell (GHC 7.10.3) (judge verdict: Accepted)

import           Control.Applicative
import           Control.DeepSeq
import           Control.Monad
import           Control.Monad.ST
import qualified Data.Array                    as A
import qualified Data.Array.IArray             as IA
import qualified Data.Array.IO                 as AI
import qualified Data.Array.MArray             as MA
import qualified Data.Array.ST                 as STA
import qualified Data.Array.Unboxed            as AU
import           Data.Bits
import qualified Data.ByteString.Char8         as BS
import           Data.Char
import qualified Data.Graph                    as G
import           Data.Int
import qualified Data.IntMap                   as IM
import qualified Data.IntSet                   as IS
import           Data.List
import qualified Data.Map.Strict               as M
import           Data.Maybe
import           Data.Ord
import qualified Data.Sequence                 as SQ
import qualified Data.Set                      as S
import           Data.Time
import qualified Data.Tree                     as T
import qualified Data.Vector                   as V
import qualified Data.Vector.Mutable           as VM
import qualified Data.Vector.Unboxed           as VU
import qualified Data.Vector.Unboxed.Mutable   as VUM

readInt :: IO Int
readInt = fst . fromJust . BS.readInt <$> BS.getLine

readInts :: IO [Int]
readInts = map (fst . fromJust . BS.readInt) . BS.words <$> BS.getLine

readIntLists :: Int -> IO [[Int]]
readIntLists n = replicateM n readInts

readInteger :: IO Integer
readInteger = fst . fromJust . BS.readInteger <$> BS.getLine

readIntegers :: IO [Integer]
readIntegers = map (fst . fromJust . BS.readInteger) . BS.words <$> BS.getLine

readIntegerLists :: Int -> IO [[Integer]]
readIntegerLists n = replicateM n readIntegers

readStrings :: IO [String]
readStrings = map BS.unpack . BS.words <$> BS.getLine

readStringLists :: Int -> IO [[String]]
readStringLists n = replicateM n <$> readStrings

toPair :: [a] -> (a, a)
toPair [x, y] = (x, y)

count :: Eq a => a -> [a] -> Int
count a as = length $ filter (== a) as

put :: Show a => a -> IO ()
put = putStr . show

putList :: Show a => [a] -> IO ()
putList [n     ] = print n
putList (n : ns) = do
  put n
  putStr " "
  putList ns

putStrList :: [String] -> IO ()
putStrList [n     ] = putStrLn n
putStrList (n : ns) = do
  putStr n
  putStr " "
  putStrList ns

yesNoUpper b | b         = putStrLn "YES"
             | otherwise = putStrLn "NO"

yesNo b | b         = putStrLn "Yes"
        | otherwise = putStrLn "No"

divCeiling x n | b == 0    = a
               | otherwise = a + 1
  where (a, b) = x `divMod` n

main = do
  [a, b, k] <- readInts
  let ms = [x | x<-[100,99..],a `mod` x==0,b`mod`x==0] in print $ ms !! (k-1)