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: Wrong Answer)

use std::io;
use std::str::FromStr;

fn input_tuple() -> (u64, u64, u64) {
    let mut line: String = String::new();
    io::stdin().read_line(&mut line);
    let vec: Vec<u64> = line.split_whitespace().map(|s| s.parse().unwrap()).collect();
    (vec[0], vec[1], vec[2])
}


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

fn divisors(n: u64) -> Vec<u64> {
    let mut divisors: Vec<u64> = Vec::new();
    for i in 1..(n+1) {
        if i * i > n {
            break;
        }
        if n % i == 0 {
            divisors.push(i);
            if i * i != n {
                divisors.push(n / i);
            }
        }
    }
    divisors
}

fn main() {
    let (a, b, k) = input_tuple();
    let mut divisors = divisors(gcd(a, b));
    divisors.sort();
    println!("{:?}", divisors[(k-1) as usize]);
}