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)


fn getline() -> String{
	let mut __ret=String::new();
	std::io::stdin().read_line(&mut __ret).ok();
	return __ret;
}



fn main() {
    let line = getline();

    let vec: Vec<&str> = line.split_whitespace().collect();
    let a:i32  = vec[0].parse().unwrap_or(0);
    let b:i32  = vec[1].parse().unwrap_or(0);
    let mut k:i32  = vec[2].parse().unwrap_or(0);

    let mut ans:i32 = 0;
    for x in (1..std::cmp::min(a,b)+1).rev() {
        if a%x == 0 && b%x == 0{
            k-=1;
            if k==0{
                ans=x;
                break;
            }
        }
    }

    println!("{}", ans);
}