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)

#[allow(unused_imports)]
use std::cmp::{max, min, Ordering};
#[allow(unused_imports)]
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
#[allow(unused_imports)]
use std::io::prelude::BufRead;
#[allow(unused_imports)]
use std::io::{stdin, stdout, BufReader, BufWriter, Write};
#[allow(unused_imports)]
use std::mem::swap;
#[allow(unused_imports)]
use std::str::FromStr;
 
 
fn main() {
    let line = read_vector::<usize>();
    let (a, b, k) = (line[0], line[1], line[2]);
    let mut count = 0;
    for i in (1..101).rev() {
        if a % i == 0 && b % i == 0 {
            count += 1;
        }
        if count == k {
            println!("{}", i);
            break;
        }
    }
}
 
#[allow(dead_code)]
fn read<T>() -> T
where
    T: std::str::FromStr,
    T::Err: std::fmt::Debug,
{
    let mut buf = String::new();
    stdin().read_line(&mut buf).unwrap();
    return buf.trim().parse().unwrap();
}
 
#[allow(dead_code)]
fn read_vector<T>() -> Vec<T>
where
    T: std::str::FromStr,
    T::Err: std::fmt::Debug,
{
    let mut buf = String::with_capacity(100);
    stdin().read_line(&mut buf).unwrap();
    return buf.split_whitespace().map(|s| s.parse().unwrap()).collect();
}
 
#[allow(dead_code)]
fn read_matrix<T>() -> Vec<Vec<T>>
where
    T: std::str::FromStr,
    T::Err: std::fmt::Debug,
{
    use std::io::prelude::*;
    let stdin = stdin();
    let mut reader = BufReader::with_capacity(100 * 1024, stdin);
    let mut line = String::with_capacity(100);
    let mut matrix: Vec<Vec<T>> = Vec::new();
 
    while reader.read_line(&mut line).unwrap() > 0 {
        matrix.push(
            line.trim()
                .split_whitespace()
                .map(|s| s.parse().unwrap())
                .collect(),
        );
        line.clear();
    }
 
    return matrix;
}
 
#[allow(dead_code)]
fn read_chars() -> Vec<char> {
    let stdin = stdin();
    let mut buf = String::new();
    let _bytes = stdin.read_line(&mut buf).unwrap();
    return buf.trim().chars().collect();
}