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 Rust (1.42.0) (judge verdict: Accepted)

use proconio::{input, fastout};

macro_rules! debug {
    ($($a:expr),*) => {
        eprintln!(concat!($(stringify!($a), " = {:?}, "),*), $($a),*);
    }
}

fn gcd(mut a: usize, mut b: usize) -> usize {
    if a<b {
        let mut tmp = a;
        a = b;
        b = tmp;
    } 
    let mut r = a % b;
    while r!=0 {
        a = b;
        b = r;
        r = a % b;
    }
    b
}

#[fastout]
fn main() {
    input!{
        mut a: usize,
        mut b: usize,
        k: usize,
    }

    let d = gcd(a,b);
    let mut cnt = 1;
    debug!(d);
    for i in (1..d+1).rev() {
        if d%i==0 {
            if cnt==k {
                println!("{}", i);
                return;
            }
            cnt += 1;
        }
    }
}