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: Wrong Answer)

function main(arg) {
	arg = arg.split("\n")[0].split(" ").map(Number)
	var a = arg[0]
	var b = arg[1]
	var k = arg[2]

	var result = []
	var max = (a > b) ? a : b

	for (var i = 0; i <= max; i++) {
		if (a % i === 0 && b % i === 0) {
			result.push(i)
		}
	}
	result = result.sort((a,b => b-a))
	console.log(result[k - 1])
}
main(require('fs').readFileSync('/dev/stdin', 'utf8'));