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)

import java.util.*

fun gcd(x: Int, y: Int): Int {
    var a = x
    var b = y
    if (b > a) {
        a = y
        b = x
    }
    var c = a % b
    while (c != 0) {
        a = b
        b = c
        c = a % b
    }
    return b
}

fun main(args: Array<String>){
	val cin = Scanner(System.`in`)
    val a = cin.nextInt()
    val b = cin.nextInt()
    val k = cin.nextInt()
    
    var count = 0

    for (i in 0..99) {
        val j = 100 - i
        if (a % j == 0 && b % j == 0) {
            count += 1
        }
        if (count == k) {
            println(j)
            return
        }
    }
}