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)

use std::cmp::min;

fn get_line() -> String {
    let mut line = String::new();
    std::io::stdin().read_line(&mut line).unwrap();
    line.trim().to_string()
}

fn main() {
    let nums = get_line().split_whitespace()
        .map(|n| n.parse().unwrap())
        .collect::<Vec<u64>>();
    let (a, b, k) = (nums[0], nums[1], nums[2]);
    let mut result: Vec<u64> = Vec::new();

    for i in 1..min(a, b) + 1 {
        if a % i == 0 && b % i == 0 { result.push(i); }
    }
    result.sort_by(|a, b| b.cmp(a));
    println!("{}", result[(k - 1) as usize]);
}