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 JavaScript (node.js v5.12) (judge verdict: Runtime Error)

function main(lines) {
    const input = lines.split(' ').map(Number)
    const A = input[0]
    const B = input[1]
    const order = input[2]
    
    var divisorA = []
    var divisorB = []
    for(var i=1; i<=A; i++){
        if(A%i === 0){
            divisorA.push(i)
        }
    }
        
    for(var i=1; i<=B; i++){
        if(B%i === 0){
            divisorB.push(i)
        }
    }

    var divisorAB = divisorA.filter(function(element){return divisorB.includes(element);})
    
    console.log(divisorAB[divisorAB.length-(order)])
}

main(require('fs').readFileSync('/dev/stdin', 'utf8'));