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: Wrong Answer)

import java.util.*

fun main(args: Array<String>) {
    val sc = Scanner(System.`in`)
    val a = sc.nextInt()
    val b = sc.nextInt()
    val c = sc.nextInt()

    val alst = mutableListOf<Int>()
    for (i in 0 until a+1) {
        if (i == 0) continue
        if (a % i == 0) {
            alst.add(i)
        }
    }
    val blst = mutableListOf<Int>()
    for (i in 0 until b+1) {
        if (i == 0) continue
        if (b % i == 0) {
            blst.add(i)
        }
    }

    val lst = mutableListOf<Int>()
    alst.forEach { atai ->
        blst.forEach { batai ->
            if (atai == batai) {
                lst.add(atai)
            }
        }
    }
    println(alst[c-1])
}