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<bits/stdc++.h>
using namespace std;
#define rep0(i,n) for(i=0;i<n;i++)
#define test(a) cout << "*" << a << endl
int main(){
  int a,b;
  int kAns;
  int k=0;
  int i;
  int aBig,aSmall;
  int maxYakusuu;
  
  cin >> a >> b >> kAns;

    aBig = max(a,b);
    aSmall = min(a,b);
 
  for(i=aSmall;i>0;i--){
    if(aBig%i==0 && aSmall%i==0){
      maxYakusuu = i;
      break;/*ちゅうい*/
    }
  }
  //test(maxYakusuu);
  for(i=maxYakusuu;i>0;i--){
    if(maxYakusuu%i==0)
      k++;
    if(k==kAns){
      cout << i << endl;
      break;
    }
  }

}