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)

//b.c B-K-th Common Divisor
#include<stdio.h>

int min(int a,int b){
    if(a>b){
        return b;
    }
    return a;
}

int main(void){
    int a,b,k;
    scanf("%d %d %d",&a,&b,&k);

    int num = 0,i=min(a,b),ans;
    while(1){
        if(a%i==0 && b%i==0){
            num++;
            ans = i;
        }
        if(num == k){
            break;
        }
        i--;
    }

    printf("%d\n",ans);
    return 0;
}