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: Wrong Answer)

'use strict'

const gcd = (m, n) => {
  return n ? gcd(n, m % n) : m
}
function main(input) {
  input = input.split(' ').map(v => ~~v)

  const a = input[0]
  const b = input[1]
  const k = input[2]
  let cnt = 0
//   console.log(a, b, k)

  for (let i = 1; i <= 100; i++) {
    if (a % i == 0 && b % i == 0) {
      cnt++
    //   console.log(cnt, i)

      if (cnt == k) {
        console.log(i)
        return
      }
    }
  }

  //   console.log(gcd(input[0], input[1]))
  //   console.log(Math.min(cnt, input[2]))
}
main(require('fs').readFileSync('/dev/stdin', 'utf8'))