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>
#include <stdio.h>

#include <string>

#include <vector>
#include <list>
#include <map>

#include <algorithm>
#include <utility>

using namespace std;

int main(const int argc, const char **argv){
  int A, B, K;
  scanf("%d %d %d", &A, &B, &K);

  int count = 0;

  for(int i = 100; i > 0 ; i--){
    if(A % i == 0 && B % i == 0){
      count++;
      if(count == K){
        printf("%d", i);
        return 0;
      }
    }
  }

  return 0;
}