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 9.2.1) (judge verdict: Runtime Error)

#include<stdio.h>

int main()
{
    int A,B,K,i,x;
    int div[10];
    int n=0;
    scanf("%d %d %d", &A, &B, &K);
    if(A<B)
        x = A;
    else
        x=B;
    
    n=0;
    for(i=1; i<=x; i++)
    {
        if(A%i==0 && B%i==0)
        {
            div[n]=i;
            n++;
        }


    }

    printf("%d", div[K-1]);

    return 0;

}