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: Runtime Error)

#include<stdio.h>
#include<stdlib.h>
#include<string.h>

int main()
{
    int a,b,k;
    int i;
    int r;
        int l;

    int j=1;
    int x[101] = {0};
    int y[101] = {0};
    int z[101] = {0};

    // スペース区切りの整数の入力
    scanf("%d %d %d",&a,&b,&k);

   for(i=1;i<=100;i++){
        if(a % i == 0){
              x[i]++;
              printf("x %d\n",i);
        }
   }

   for(i=1;i<=100;i++){
        if(b % i == 0){
              y[i]++;
             printf("y %d\n",i);
        }
   }

   for(i=1;i<=100;i++){
        for(l=1;l<=100;l++){
        if(x[i] == y[l]){
              z[j] = x[i];
              j++;
        }
        if((k+1) == j){
            break;
        }
   }
   }
   
    // 出力
    printf("%d\n",z[k]);
    return 0;
}