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(){
  int A, B, K;
  scanf("%d %d %d", &A, &B, &K);

  int G;

  while(A != 0 && B != 0){
    if(A == 1 || B == 1) break;

    if(A >= B) A = A % B;
    else B = B % A;
  }

  if(A == 0) G = B;
  else if(B == 0) G = A;
  else G = 1;

  int i = 0;
  int j = 1;
  int L[K];
  while(i < K){
    if(G % j == 0){
      L[i] = G / j;
      i++;
    }
    j++;
  }

  printf("%d\n", L[K-1]);


  return 0;
}