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";

function Main(input) {
	input = input.split(" ");
    const a = parseInt(input[0], 10);
    const b = parseInt(input[1], 10);
    const k = parseInt(input[2], 10);

    let candidateCount = 0;
    let answer = 0;
    for (let i = 100; i > 0; i--) {
        if (a % i == 0 && b % i == 0) {
            candidateCount++;
        }

        if (candidateCount == k) {
            answer = i;
            break;
        }
    }

    console.log(answer);
}

Main(require("fs").readFileSync("/dev/stdin", "utf8"));