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>
#include <stdlib.h>
#include <string.h>
#include <ctype.h>
#include <math.h>

int main(){
    int a,b,k,ans,count=0,kotae;
    scanf("%d%d%d",&a,&b,&k);
    if (a>=b) {
        ans=b;
    }else{
        ans=a;
    }
    for (int i=ans; count!=k; i--) {
        if (a%i==0&&b%i==0) { //aの約数でかつbの約数
            kotae=i;
            count++;
        }
    }
    printf("%d\n",kotae);
    return 0;
}