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, c, k = 0, r, tmp, cnt=0;
    
    scanf("%d%d%d", &a, &b, &c);
    /* 自然数 a > b を確認・入替 */
    if(a<b){
        tmp = a;
        a = b;
        b = tmp;
    }
    
    /* ユークリッドの互除法 */
    r = a % b;
    while(r!=0){
        a = b;
        b = r;
        r = a % b;
    }
    
    /* 最大公約数を出力 */
    printf("最大公約数 = %d\n", b);
    
    
    int i;
    
    
    for( i=1; i<=b; ++i ){
        if( b%i == 0 ){
            cnt++;
        }
    }
    /* 約数を求める */
    for( i=1; i<=b; ++i ){
        if( b%i == 0 ){
            if(k==cnt-c){
                //printf("k = %d\n", k);
                //printf("cnt = %d\n", cnt);
                printf("%d\n", i);
            }
            k++;
        }
    }
    return 0;
}