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,n;
 scanf("%d%d%d",&a,&b,&c);
 if(a<1 || b<1 || c<1 || a>100 || b>100 || c>100)
   printf("正しい値を入力してください。\n");
 n=b/a;
 if(n>c){
   printf("%d\n",c);
   printf("高橋くんは%d円以上持っているのでお気に入りの音を%d回聞いて満足します>。\n",a*c,c);
 }
 else if(n<c){
   printf("%d\n",n);
   printf("高橋くんが満足できないこともあります。\n");
 }
 return 0;
}