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 gcd(x: u32, y: u32) -> u32 {
    let mut x = x;
    let mut y = y;
    while y != 0 {
        let t = y;
        y = x % y;
        x = t;
    }
    x
}

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_line(&mut buf).unwrap();
    let mut iter = buf.split_whitespace();
    let a: u32 = iter.next().unwrap().parse().unwrap();
    let b: u32 = iter.next().unwrap().parse().unwrap();
    let mut k: u32 = iter.next().unwrap().parse().unwrap();

    let ab_gcd = gcd(a, b);

    for i in (0..ab_gcd+1).rev() {
        if ab_gcd % i == 0 {
            k -= 1;
        }
        if k == 0 {
            println!("{}", i);
            break;
        }
    }
}