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 gcd(a: Int, b:Int):Int = if (b == 0) {a} else {gcd(b, a % b)}
fun main(args:Array<String>) {
    val (A,B,K) = readLine()!!.split(" ").map(String::toInt)

    val gcdAB = gcd(A,B)

    (1..gcdAB).filter { 
        A % it == 0 && B % it == 0
    }.sortedDescending().take(K).last().run(::println)

}