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 (b > a){
        int tmp = a;
        a = b;
        b = tmp;
    }
    int r = a % b;
    while(r > 0){
        a = b;
        b = r;
        r = a % b;
    }
    return b;
}

int k_divisor(int A, int K){
    int count = 0;
    int ans = 0;
    for (int i = A; i > 0; i--){
        if(A % i == 0){
            count += 1;
        }
        if(count == K){
            ans = i;
            break;
        }
    }
    return ans;
}

int main(void){
    int A, B, K;
    scanf("%d %d %d", &A, &B, &K);
    int g = gcd(A, B);
    int ans = k_divisor(g, K);
    printf("%d\n", ans);
    return 0; 
}