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 main(void){
  int a, b, k;
  scanf("%d %d %d", &a, &b, &k);
  int C[100];
  int c = 0, count = 0;
  if(a >= b){
    for(int i = 1; i <= a; i++)
      if(a%i == 0 && b%i == 0){
        C[c++] = i;
        count++;
      }
  }
  else {
    for(int i = 1; i <= b; i++)
      if(a%i == 0 && b%i == 0){
        C[c++] = i;
        count++;
      }
    }
  printf("%d", C[count-k]);
}