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 N(int A, int B, int K){
  int n, c;
  c = 0;
  for(n = 100;n > 0;n--){
    if(A % n + B % n == 0) c++;
    if(c == K) break;
  }
  return n;
}

int main(void){
  int A, B, K;
  scanf("%d %d %d", &A, &B, &K);
  printf("%d\n", N(A, B, K));
  return 0;
}