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 (1.15.1) (judge verdict: Accepted)

use std::io::stdin;

macro_rules! read {
    ($t: ty) => {{
        let mut line = String::new();
        stdin().read_line(&mut line);
        line.trim().parse::<$t>().unwrap()
    }};
    ($($t: ty), *) => {{
        let mut line = String::new();
        stdin().read_line(&mut line);
        let mut iter = line.split_whitespace();
        (
            $(iter.next().unwrap().parse::<$t>().unwrap(), )*
        )
    }}
}
macro_rules! reads {
    ($e:expr, $t:ty) => {{
        let mut v = vec![];
        for _ in 0..$e {
            let mut line = String::new();
            stdin().read_line(&mut line);
            v.push(line.trim().parse::<$t>().unwrap());
        }
        v
    }};
}

fn main() {
    let (a, b, k) = read!(u32, u32, u32);

    let mut n = 101;
    for _ in 0..k {
        for i in (1..n).rev() {
            if a % i == 0 && b % i == 0 {
                n = i;
                break;
            }
        }
    }
    println!("{}", n);
}