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 (1.3.71) (judge verdict: Wrong Answer)

import kotlin.math.max
import kotlin.math.min

fun main() {
    val (A, B, K) = readLine()!!.split(" ").map { it.toInt() }
    val C = min(A, B)
    var list = mutableListOf<Int>()

    for (i in 1..(C/2)) {
        if (C % i == 0) {
            list.add(i)
        }
    }

    if (max(A, B) % C == 0) {
        list.add(C)
    }

    val ans = list.sortedDescending()[K-1]

    println(ans)
}