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 (GCC 5.4.1) (judge verdict: Accepted)

#include<stdio.h>
int main(void)
{
  int A,B,K,cnt=0;
  scanf("%d%d%d",&A,&B,&K);
  
  if(A>B){
    for(int i=A;i>=1;i--){
      if((A%i==0) && (B%i==0)){
        cnt++;
        if(cnt==K){
          printf("%d",i);
        }
      }
    }
  }else{
    for(int i=B;i>=1;i--){
      if((A%i==0) && (B%i==0)){
        cnt++;
        if(cnt==K){
          printf("%d",i);
        }
      }
  	}   
  }
  
  return 0;
}