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 Ruby (2.3.3) (judge verdict: Accepted)

=begin
－－－－－－－－－－－－－－
  A, B = 入力値
  min = AとBの小さい方
  ans = AとBを割り切れる正整数の配列
  K = ansのindex
－－－－－－－－－－－－－－
  1: 1 ~ (AとBの小さい方の値)までループする(i)
    i が AとB を...
    割り切れる場合: ans に 挿入
    割り切れない場合: 次の i へ
  2: ans の K 番目に"大きな"要素を出力
=end

A, B, K = gets.split.map(&:to_i);
min = [A,B].min;
ans = [];

for i in 1..A do
  if A % i == 0 && B % i == 0
    ans << i
  end
end

puts ans[-K];