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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
#define ll long long
const int MAXN=1e5+5;
const int MOD=1e9+7;
using namespace std;

int main(){
	int a, b, k;
	int tmp;
	int cnt=0;
	scanf("%d%d%d",&a,&b,&k);
	tmp=min(a, b);
	for(int i=tmp;i>=1;i--){
		if(a%i==0&&b%i==0){
			cnt++;
		}
		if(cnt==k){
			printf("%d", i);
			break;
		}
	
	}
	return 0;
}