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)

#![allow(
    non_snake_case,
    unused_variables,
    unused_assignments,
    unused_mut,
    dead_code
)]
use proconio::input;
//use proconio::marker::Usize1;
//use proconio::marker::Chars;
//use std::collections::HashSet;
use std::cmp::*;
fn main() {
    input! {
        a:i32,b:i32, mut k:i32
    }
    for i in (1..(min(a, b) + 1)).rev() {
        if a % i == 0 && b % i == 0 {
            k -= 1;
            if k == 0 {
                println!("{}", i);
            }
        }
    }
}