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 get_input() -> String {
    let mut word = String::new();
    std::io::stdin().read_line(&mut word).unwrap();
    word.trim().to_owned()
}

fn main() {
    let (a,b,k) = {
        let line = get_input();
        let mut split = line.split_whitespace();
        let a:i64 = split.next().unwrap().parse().unwrap();
        let b:i64 = split.next().unwrap().parse().unwrap();
        let k:i64 = split.next().unwrap().parse().unwrap();
        (a,b,k)
    };

    let mut ans = 0;
    let min = std::cmp::min(a,b);

    for i in (1..min+1).rev() {
        if a % i == 0 && b % i == 0 {
            ans += 1;
            if ans >= k {
                println!("{}", i);
                break;
            }
        }
    }
}