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};

#[fastout]
fn main() {
    input! {
        a: usize,
        b: usize,
        k: usize
    };

    let x1 = if a > b { a } else { b };
    let x2 = if a > b { b } else { a };

    let mut count = 0;
    let mut y = x1;

    while x1 > 0 {
        let z1 = x1 / y;
        let z2 = x2 / y;

        if z1 * y == x1 && z2 * y == x2 {
            count += 1;
        }
        if count == k {
            println!("{}", y);
            break;
        }

        y -= 1;
    }
}