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 Kotlin (1.0.0) (judge verdict: Accepted)

fun main (args : Array<String>) {
	val (a, b, k) = readLine()!!.split(" ").map(String::toInt)
	val A : Int = a.toInt()
	val B : Int = b.toInt()
	val K : Int = k.toInt()
	var result : MutableList<Int> = mutableListOf()
	for (i in 1..100) {
		if ( (A % i == 0) && (B % i == 0) ) {
			result.add(i)
		}
	}
	result.reverse()
	println("${result[K - 1]}")
}