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)

#[allow(unused)]
use std::{io, str, vec};

#[allow(unused)]
fn read<T: str::FromStr>() -> T {
    let mut s = String::new();
    io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

#[allow(unused)]
fn read_vec<T: str::FromStr>() -> Vec<T> {
    read::<String>().split_whitespace()
        .map(|e| e.parse().ok().unwrap()).collect()
}

#[allow(unused)]
fn read_vec2<T: str::FromStr>(n: u32) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}

fn main() {
    let v: Vec<usize> = read_vec();
    
    let mut count = 0;
    for i in (1..v[1]+1).rev() {
        if v[0]%i == 0 {
            if v[1]%i == 0 {
                count += 1;
                if count == v[2] {
                    println!("{:?}", i);
                    break;
                    }
            }
        }
    }
}