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: Wrong Answer)

#include<stdio.h>
int main(void){
    int a,b,k;
    scanf("%d%d%d",&a,&b,&k);
    int p[k],q=a>b?b:a;
    for(int i=0;k>i;++i)
    p[i]=0;
    int c=0;
    for(int i=0;q>i;++i)
    if(a%(i+1)==0&&b%(i+1)==0){
        p[c]=i+1;
        ++c;
    }
    printf("%d",p[k-1]);
    return 0;
}