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 JavaScript (node.js v5.12) (judge verdict: Accepted)

"use strict";

const main = arg => {
    const A = parseInt(arg.split("\n")[0].split(" ")[0]);
    const B = parseInt(arg.split("\n")[0].split(" ")[1]);
    const K = parseInt(arg.split("\n")[0].split(" ")[2]);
    const list = [];
    
    for(let i=1; i<=Math.min(A,B); i++) {
        if(A % i == 0 && B % i == 0) {
            list.push(i);
        }
    }
    
    console.log(list[list.length - K]);
}
main(require('fs').readFileSync('/dev/stdin', 'utf8'));