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)

fn main() {
    use std::io::Read;
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();
    let mut iter = buf.split_whitespace();
    
    let a: u64 = iter.next().unwrap().parse::<u64>().unwrap();
    let b: u64 = iter.next().unwrap().parse::<u64>().unwrap();
    let k: usize = iter.next().unwrap().parse::<usize>().unwrap();
    
    let g = gcd(a, b);
    let mut divs = divisors(g);
    divs.sort();
    divs.reverse();
    println!("{}", divs[k-1]);
}

#[allow(dead_code)]
pub fn gcd(a: u64, b: u64) -> u64 {
    if b == 0 {
        a
    } else {
        gcd(b, a % b)
    }
}

#[doc = " n>=1"]
#[allow(dead_code)]
fn divisors(n: u64) -> Vec<u64> {
    let mut ret = vec![];
    {
        let mut i = 1;
        while i * i <= n {
            if n % i == 0 {
                ret.push(i);
                if i != n / i {
                    ret.push(n / i);
                }
            }
            i += 1;
        }
    }
    ret
}