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)

// 日本語
use std::io::stdin;

fn main() {
    let mut s = String::new();
    stdin().read_line(&mut s).ok();
    let vs: Vec<u64> = s.trim().split_whitespace().map(|token| token.parse().ok().unwrap()).collect();
    let a = vs[0];
    let b = vs[1];
    let k = vs[2];

    let mut n = 0;
    for i in (1..gcd(a, b)+1).rev() {
        if a % i == 0 && b % i == 0 {
            n += 1;
            if n == k {
                println!("{}", i);
                break;
            }
        }
    }
}

fn gcd(a: u64, b: u64) -> u64 {
    if b == 0 {
        a
    } else {
        gcd(b, a % b)
    }
}