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)

module Main where

import qualified Data.Vector as V 
import qualified Data.Map as M
import Control.Monad
import Data.Maybe
readint :: IO Int
readint = read <$> getLine

readvec :: IO [Int]
readvec = (fmap read . words) <$> getLine

main :: IO()
main = do
  [a,b,k] <- readvec
  l <- forM [1..100] $ \i -> do
    if a `mod` i == 0 && b `mod` i == 0
       then pure $ Just i
       else pure Nothing
  -- print $ catMaybes l
  print $ (reverse $ catMaybes l) !! (k-1)