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.Monad
import           Control.Monad.ST
import qualified Data.Array                    as A
import qualified Data.Array.ST                 as ST
import qualified Data.Array.Unboxed            as AU
import qualified Data.ByteString.Char8         as BS
import           Data.Char
import qualified Data.Foldable                 as DF
import           Data.Int
import qualified Data.IntMap                   as IM
import           Data.List
import qualified Data.Map                      as M
import           Data.Maybe
import           Data.Ord
import qualified Data.Set                      as S
import qualified Data.Sequence                 as SQ
import           Data.Time
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 = map (fst . fromJust . BS.readInt) . BS.words <$> BS.getLine
readInts n = replicateM n readInt
readString = map BS.unpack . BS.words <$> BS.getLine
readStrings n = replicateM n <$> readString
toPair [x, y] = (x, y)

main = do
  [a, b, k] <- readInt
  print $ solve a b k

solve a b k = reverse (filter (\x -> f x a b) [1 .. max a b]) !! (k - 1)

f :: Int -> Int -> Int -> Bool
f n a b = (a `mod` n == 0) && (b `mod` n == 0)