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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>

uint32_t gcd(uint32_t a, uint32_t b) {
  if (b == 0) return a;
  return gcd(b, b % a);
}

int main() {
  uint32_t A = 0, B = 0, K = 0;
  std::cin >> A >> B >> K;

  uint32_t k = 0, cd = gcd(A, B);
  while (cd > 0) {
    if (A % cd == 0 && B % cd == 0) k++;
    if (k == K) {
      std::cout << cd << std::endl;
      break;
    }
    cd--;
  }

  return 0;
}