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)

{-# OPTIONS_GHC -O2 -funbox-strict-fields #-}

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

solve :: Int -> Int -> Int -> Int
solve a b k = [i | i <- reverse [1 .. min a b], divisible a b i] !! (k - 1)

divisible :: Int -> Int -> Int -> Bool
divisible a b i = a `mod` i == 0 && b `mod` i == 0