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() {
    let (a, b, k) = {
        let mut line = String::new();
        std::io::stdin().read_line(&mut line).unwrap();
        let mut ws = line.split_whitespace();
        let a: i32 = ws.next().unwrap().parse().unwrap();
        let b: i32 = ws.next().unwrap().parse().unwrap();
        let k: i32 = ws.next().unwrap().parse().unwrap();
        (a, b, k)
    };
    let list = (1 .. std::cmp::min(a, b) + 1)
        .filter(|x| a % x == 0 && b % x == 0)
        .collect::<Vec<i32>>();
    println!("{}", list[(list.len() as i32 - k) as usize]);
}