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

int main(){
  int a,b,k;
  scanf("%d %d %d",&a,&b,&k);
  int d=gcd(a,b),i=0;
  while(k){
    i++;
    if(d%i==0) k--;
  }
  printf("%d",d/i);
}