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)


// problem: "https://atcoder.jp/contests/abc120/tasks/abc120_b"

#include<iostream>

using namespace std;

int gcd(int a,int b)
{
    if(b==0)
        return a;

    return gcd(b,a%b);
}

int main()
{
    int A,B,K;
    cin>>A>>B>>K;

    int g = gcd(max(A,B),min(A,B));
    int k,i;
    k = 0;
    for(i=g;i>0;i--)
    {
        if(g%i==0)
            k++;

        if(k==K)
            break;
    }

    cout<<i;

    return 0;
}