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 Julia (0.5.0) (judge verdict: Wrong Answer)

parseInt(x) = parse(Int,x)
parseMap(x::Array{SubString{String}, 1}) = map(parseInt, x)
function main()
    a,b,k = map(parseInt, split(readline()))
  ans = zeros(maximum([a b]));
  c  =1
  for i = 1:maximum([a b])
    if mod(a,i) == 0 && mod(b,i) == 0
      ans[c] = i
      c +=1
    end
  end
  println(Int64(ans[end-k+1]))
end
main()