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;

// 入力関数
fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

// 以下main
fn main() {
    let init: Vec<u32> = read_vec();
    let a = init[0];
    let b = init[1];
    let k = init[2] as usize;

    let mut divisor: Vec<u32> = Vec::new();

    for i in 0..cmp::min(a, b) {
        let devider = i + 1 as u32;
        if a % devider == 0 && b % devider == 0 {
            divisor.push(devider);
        }
    }

    let n = divisor.len();

    if n != 0 {
        println!("{}", divisor[n - k]);
    } else {
        println!("{}", 1);
    }
}