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)

main :: IO ()
main = do
  [a,b,k] <- map (read :: String -> Int) . words <$> getLine
  print $ ans a b k

ans :: Int -> Int -> Int -> Int
ans a b k = (!! (k-1)) $ foldl (\acc k -> if mod g k == 0 then (div g k) : acc else acc) [] [g,g-1..1] where
  g = gcd a b