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 <string.h>
#include <algorithm>
#include <vector>
#include <string>
#include <tuple>
using namespace std;
int main(void){
  int A,B,K;
  cin>>A>>B>>K;
  int count=0;
  for(int i=1;i<=100;i++){
    if(A%i==0&&B%i==0){ count++; }
  }
  int ans=0;
  for(int i=1;i<=100;i++){
      if(A%i==0&&B%i==0){ans++; if(ans==count-K+1){cout<<i; break;}}
  }
    return 0;
}