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>
#include <stdlib.h>

int gcc(int a, int b){
    if(a<b){
        int tmp = a;
        a = b;
        b = tmp;
    }
    int r = a % b;
    while(r!=0){
        a = b;
        b = r;
        r = a % b;
    }
    return b;
}

int main(){
    int a, b, i, j, k;
    int cc[100] = {0};
    scanf("%d %d %d", &a, &b, &k);
    int g = gcc(a, b);
    j = 0;
    for(i=g;i>=2;i--){
        if(g % i == 0){
            cc[j] = i;
            j++;
        }
    }
    int x = cc[k-1];
    printf("%d", x);
    return 0;
}