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(){
	int A,B,K;
  	int i,sum=0;
  	int wari[150]={0};

  
  if(scanf("%d %d %d", &A,&B,&K) < 3) {
    fprintf(stderr, "error: ill-formed fraction.\n");
}
  
  for(i=1;i<=110;i++){
  	if(A%i == 0 && B%i ==0) wari[i]=1;
    else;
    //printf("wari[%d]%d ",i,wari[i]);
  }
  
  
  for(i=1;i<=110;i++){
  	sum+=wari[i];
    if(sum==K) break;
    else;
  }
  
  printf("%d",i);
  
  return 0;
}