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 (1.42.0) (judge verdict: Accepted)

use proconio::{fastout, input};
use std::cmp::min;
#[allow(unused_mut)]
#[fastout]
fn main() {
    input! {
        a: usize,
        b: usize,
        k: usize
    }
    let mut div = Vec::new();
    for i in 1..=min(a, b) {
        if a % i == 0 && b % i == 0 {
            div.push(i);
        }
    }
    div.reverse();
    println!("{}", div[k - 1]);
}